id
string | text
string | len_category
string | source
string |
|---|---|---|---|
math/0302053
|
We prove that ribbons, i.e. double structures associated with a line bundle
$\SE$ over its reduced support, a smooth irreducible projective curve of
arbitrary genus, are smoothable if their arithmetic genus is greater than or
equal to $3 $ and the support curve possesses a smooth irreducible double cover
with trace zero module $\SE$. The method we use is based on the infinitesimal
techniques that we develop to show that if the support curve admits such a
double cover then every embedded ribbon over the curve is ``infinitesimally
smoothable'', i.e. the ribbon can be obtained as central fiber of the image of
some first--order infinitesimal deformation of the map obtained by composing
the double cover with the embedding of the reduced support in the ambient
projective space containing the ribbon. We also obtain embeddings in the same
projective space for all ribbons associated with $\SE$. Then, assuming the
existence of the double cover, we prove that the ``infinitesimal smoothing''
can be extended to a global embedded smoothing for embedded ribbons of
arithmetic genus greater than or equal to 3. As a consequence we obtain the
smoothing results.
|
256
|
arxiv_abstracts
|
math/0302054
|
In this paper we shall define the analytic continuation of the multiple
polylogarithms by using Chen's theory of iterated path integrals and compute
the monodromy of all multiple logarithms explicitly.
|
lt256
|
arxiv_abstracts
|
math/0302055
|
It's well known that multiple polylogarithms give rise to good unipotent
variations of mixed Hodge-Tate structures. In this paper we shall {\em
explicitly} determine these structures related to multiple logarithms and some
other multiple polylogarithms of lower weights. The purpose of this explicit
construction is to give some important applications: First we study of the
limit mixed Hodge-Tate structures and make a conjecture relating the variations
of mixed Hodge-Tate structures of multiple logarithms to those of general
multiple {\em poly}logarithms. Then following Deligne and Beilinson we describe
an approach to defining the single-valued real analytic version of the multiple
polylogarithms which generalizes the well-known result of Zagier on classical
polylogarithms. In the process we find some interesting identities relating
single-valued multiple polylogarithms of the same weight $k$ when $k=2$ and 3.
At the end of this paper, motivated by Zagier's conjecture we pose a problem
which relates the special values of multiple Dedekind zeta functions of a
number field to the single-valued version of multiple polylogarithms.
|
256
|
arxiv_abstracts
|
math/0302056
|
We analyze the general problem of determining optimally dense packings, in a
Euclidean or hyperbolic space, of congruent copies of some fixed finite set of
bodies. We are strongly guided by examples of aperiodic tilings in Euclidean
space and a detailed analysis of a new family of examples in the hyperbolic
plane. Our goal is to understand qualitative features of such optimum density
problems, in particular the appropriate meaning of the uniqueness of solutions,
and the role of symmetry in classfying optimally dense packings.
|
lt256
|
arxiv_abstracts
|
math/0302057
|
We survey some recent results concerning the behaviour of the contact
structure defined on the boundary of a complex isolated hypersurface
singularity or on the boundary at infinity of a complex polynomial.
|
lt256
|
arxiv_abstracts
|
math/0302058
|
We give an introduction to the theory of determinantal ideals and rings,
their Groebner bases, initial ideals and algebras, respectively. The approach
is based on the straightening law and the Knuth-Robinson-Schensted
correspondence. The article contains a section treating the basic results about
the passage to initial ideals and algebras.
|
lt256
|
arxiv_abstracts
|
math/0302059
|
For some m \ge 4, let us color each column of the integer lattice L = Z^2
independently and uniformly into one of m colors. We do the same for the rows,
independently from the columns. A point of L will be called blocked if its row
and column have the same color. We say that this random configuration
percolates if there is a path in L starting at the origin, consisting of
rightward and upward unit steps, and avoiding the blocked points. As a problem
arising in distributed computing, it has been conjectured that for m \ge 4, the
configuration percolates with positive probability. This has now been proved
(in a later paper), for large m. Here, we prove that the probability that there
is percolation to distance n but not to infinity is not exponentially small in
n. This narrows the range of methods available for proving the conjecture.
|
lt256
|
arxiv_abstracts
|
math/0302060
|
The colored Jones polynomial of links has two natural normalizations: one in
which the n-colored unknot evaluates to [n+1], the quantum dimension of the
(n+1)-dimensional irreducible representation of quantum sl(2), and the other in
which it evaluates to 1. For each normalization we construct a bigraded
cohomology theory of links with the colored Jones polynomial as the Euler
characteristic.
|
lt256
|
arxiv_abstracts
|
math/0302061
|
Certain topological dynamical systems are considered that arise from actions
of $\sigma$-compact locally compact Abelian groups on compact spaces of
translation bounded measures. Such a measure dynamical system is shown to have
pure point dynamical spectrum if and only if its diffraction spectrum is pure
point.
|
lt256
|
arxiv_abstracts
|
math/0302062
|
This is the second issue of the SPM Bulletin (SPM stands for "Selection
Principles in Mathematics"). The first issue is math.GN/0301011 and contains
some background and details.
|
lt256
|
arxiv_abstracts
|
math/0302063
|
The traces of the quantum powers of a generic quantum matrix pairwise
commute. This was conjectured by Kaoru Ikeda, in connection with certain
Hamiltonian systems. The proof involves Newton's formulae for quantum matrices,
relating traces of quantum powers with sums of principal minors.
|
lt256
|
arxiv_abstracts
|
math/0302064
|
I construct some smooth Calabi-Yau threefolds in characteristic two and three
that do not lift to characteristic zero. These threefolds are pencils of
supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of
abelian surfaces and Katsura's analysis of generalized Kummer surfaces. The
threefold in characteristic two turns out to be nonrigid.
|
lt256
|
arxiv_abstracts
|
math/0302065
|
We generalize the notion of parallel transport along paths for abelian
bundles to parallel transport along surfaces for abelian gerbes using an
embedded Topological Quantum Field Theory (TQFT) approach. We show both for
bundles and gerbes with connection that there is a one-to-one correspondence
between their local description in terms of locally-defined functions and forms
and their non-local description in terms of a suitable class of embedded
TQFT's.
|
lt256
|
arxiv_abstracts
|
math/0302066
|
This article concerns the equations of motion of perfect incompressible
fluids in a 3-D, smooth, bounded, simply connected domain. We suppose that the
curl of the initial velocity field is a vortex patch, and examine the classical
problems of the existence of a solution, either locally or globally in time,
and of the persistence of the initial regularity.
|
lt256
|
arxiv_abstracts
|
math/0302067
|
We quantize the Alekseev-Meinrenken solution r to the classical dynamical
Yang-Baxter equation, associated to a Lie algebra g with an element t in
S^2(g)^g. Namely, we construct a dynamical twist J with nonabelian base in the
sense of P. Xu, whose quasiclassical limit is r-t/2. This twist gives rise to a
dynamical quantum R-matrix, and also provides a quantization of the
quasi-Poisson manifold and Poisson groupoid associated to r. The twist J is
obtained by an appropriate renormalization of the Knizhnik-Zamolodchikov
associator for g, introduced by Drinfeld.
|
lt256
|
arxiv_abstracts
|
math/0302068
|
A Calabi-Yau orbifold is locally modeled on C^n/G where G is a finite
subgroup of SL(n, C). In dimension n=3 a crepant resolution is given by
Nakamura's G-Hilbert scheme. This crepant resolution has a description as a
GIT/symplectic quotient. We use tools from global analysis to give a
geometrical generalization of the McKay Correspondence to this case.
|
lt256
|
arxiv_abstracts
|
math/0302069
|
It has been pointed out to the author by David Glickenstein that the proof of
the (closely related) Lemmas 1.2 and 3.2 in the title paper is incorrect. The
statements of both Lemmas are correct, and the purpose of this note is to give
a correct argument. The argument is of some interest in its own right.
|
lt256
|
arxiv_abstracts
|
math/0302070
|
We establish a glueing theorem for the Ginzburg-Landau equations in dimension
$n > 2$. To this end, we consider a nondegenerate minimal submanifold of
codimension 2, and construct a one-parameter family of solutions to the
Ginzburg-Landau equations such that the energy density concentrates near this
submanifold. The proof is based on a construction of suitable approximate
solutions and the implicite function theorem.
|
lt256
|
arxiv_abstracts
|
math/0302071
|
In our previous paper math.QA/9907181, to every finite dimensional
representation V of the quantum group U_q(g), we attached the trace function
F^V(\lambda,\mu), with values in End V[0], obtained by taking the (weighted)
trace in a Verma module of an intertwining operator. We showed that these trace
functions satisfy the Macdonald-Ruijsenaars and the qKZB equations, their dual
versions, and the symmetry identity. In this paper we show that the trace
functions satisfy the orthogonality relation and the qKZB-heat equation. For
g=sl_2, this statement is the trigonometric degeneration of a conjecture of
Felder and the second author, proved by them for the 3-dimensional irreducible
V. We also establish the orthogonality relation and qKZB-heat equation for
trace functions obtained by taking traces in finite dimensional representations
(rather than Verma modules). If g=sl_n and V=S^{kn}C^n, these functions are
known to be Macdonald polynomials of type A. In this case, the orthogonality
relation reduces to the Macdonald inner product identities, and the qKZB-heat
equation coincides with the q-Macdonald-Mehta identity, proved by Cherednik.
|
256
|
arxiv_abstracts
|
math/0302072
|
Let $S^{n}$ be the $n$-sphere of constant positive curvature. For $n \geq 2$,
we will show that a measure on the unit tangent bundle of $S^{2n}$, which is
even and invariant under the geodesic flow, is not uniquely determined by its
projection to $S^{2n}$.
|
lt256
|
arxiv_abstracts
|
math/0302073
|
In this paper, we investigate higher direct images of log canonical divisors.
After we reformulate Koll\'ar's torsion-free theorem, we treat the relationship
between higher direct images of log canonical divisors and the canonical
extensions of Hodge filtration of gradedly polarized variations of mixed Hodge
structures. As a corollary, we obtain a logarithmic version of
Fujita-Kawamata's semi-positivity theorem. By this semi-positivity theorem, we
generalize Kawamata's positivity theorem and apply it to the study of a log
canonical bundle formula. The final section is an appendix, which is a result
of Morihiko Saito.
|
lt256
|
arxiv_abstracts
|
math/0302074
|
Flat connections induced over covering maps are studied and the trivial ones
among them are described. In the sequel, we deal with the resulting holonomy
bundles.
|
lt256
|
arxiv_abstracts
|
math/0302075
|
We study some basic properties of the variety of characters in PSL(2,C) of a
finitely generated group. In particular we give an interpretation of its points
as characters of representations. We construct 3-manifolds whose variety of
characters has arbitrarily many components that do not lift to SL(2,C). We also
study the singular locus of the variety of characters of a free group.
|
lt256
|
arxiv_abstracts
|
math/0302076
|
We consider random walks in a random environment of the type p_0+\gamma\xi_z,
where p_0 denotes the transition probabilities of a stationary random walk on
\BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We
give an explicit expansion, for small \gamma, of the asymptotic speed of the
random walk under the annealed law, up to order 2. As an application, we
construct, in dimension d\ge2, a walk which goes faster than the stationary
walk under the mean environment.
|
lt256
|
arxiv_abstracts
|
math/0302077
|
This article accompanies my ICM talk in August 2002. Three conjectural
directions in Gromov-Witten theory are discussed: Gorenstein properties, BPS
states, and Virasoro constraints. Each points to basic structures in the
subject which are not yet understood.
|
lt256
|
arxiv_abstracts
|
math/0302078
|
Let $X$ be an integral projective scheme satisfying the condition $S_3$ of
Serre and $H^1({\mathcal O}_X(n)) = 0$ for all $n \in {\mathbb Z}$. We
generalize Rao's theorem by showing that biliaison equivalence classes of
codimension two subschemes without embedded components are in one-to-one
correspondence with pseudo-isomorphism classes of coherent sheaves on $X$
satisfying certain depth conditions.
We give a new proof and generalization of Strano's strengthening of the
Lazarsfeld--Rao property, showing that if a codimension two subscheme is not
minimal in its biliaison class, then it admits a strictly descending elementary
biliaison.
For a three-dimensional arithmetically Gorenstein scheme $X$, we show that
biliaison equivalence classes of curves are in one-to-one correspondence with
triples $(M,P,\alpha)$, up to shift, where $M$ is the Rao module, $P$ is a
maximal Cohen--Macaulay module on the homogeneous coordinate ring of $X$, and
$\alpha: P^{\vee} \to M^* \to 0$ is a surjective map of the duals.
|
lt256
|
arxiv_abstracts
|
math/0302079
|
Log-linear models are a well-established method for describing statistical
dependencies among a set of n random variables. The observed frequencies of the
n-tuples are explained by a joint probability such that its logarithm is a sum
of functions, where each function depends on as few variables as possible. We
obtain for this class a new model selection criterion using nonasymptotic
concepts of statistical learning theory. We calculate the VC dimension for the
class of k-factor log-linear models. In this way we are not only able to select
the model with the appropriate complexity, but obtain also statements on the
reliability of the estimated probability distribution. Furthermore we show that
the selection of the best model among a set of models with the same complexity
can be written as a convex optimization problem.
|
lt256
|
arxiv_abstracts
|
math/0302080
|
The Andrews-Curtis conjecture claims that every balanced presentation of the
trivial group can be reduced to the standard one by a sequence of ``elementary
transformations" which are Nielsen transformations augmented by arbitrary
conjugations. It is a prevalent opinion that this conjecture is false; however,
not many potential counterexamples are known. In this paper, we show that some
of the previously proposed examples are actually not counterexamples. We hope
that the tricks we used in constructing relevant chains of elementary
transformations will be useful to those who attempt to establish the
Andrews-Curtis equivalence in other situations.
On the other hand, we give two rather general and simple methods for
constructing balanced presentations of the trivial group; some of these
presentations can be considered potential counterexamples to the Andrews-Curtis
conjecture. One of the methods is based on a simple combinatorial idea of
composition of group presentations, whereas the other one uses "exotic" knot
diagrams of the unknot.
We also consider the Andrews-Curtis equivalence in metabelian groups and
reveal some interesting connections of relevant problems to well-known problems
in K-theory.
|
256
|
arxiv_abstracts
|
math/0302081
|
We prove the Lefchetz theorem for CR submanifolds in Hermitian symmetric
spaces. As an application we prove the nonexistence of real analytic Levi flat
submanifolds in such manifolds.
|
lt256
|
arxiv_abstracts
|
math/0302082
|
We prove that the relative commutant of a diffuse von Neumann subalgebra in a
hyperbolic group von Neumann algebra is always injective. It follows that any
non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma
and prime. The proof is based on C*-algebra theory.
|
lt256
|
arxiv_abstracts
|
math/0302083
|
We observe that a sharp result on the exponential growth rate of the number
of primitive elements exists for the free group on two generators.
|
lt256
|
arxiv_abstracts
|
math/0302084
|
Euler's transformation formula for the Gauss hypergeometric function 2F1 is
extended to hypergeometric functions of higher order. Unusually, the
generalized transformation constrains the hypergeometric function parameters
algebraically but not linearly. Its consequences for hypergeometric summation
are explored. It has as corollary a summation formula of Slater. From this
formula new one-term evaluations of 2F1(-1) and 3F2(1) are derived, by applying
transformations in the Thomae group. Their parameters are also constrained
nonlinearly. Several new one-term evaluations of 2F1(-1) with linearly
constrained parameters are derived as well.
|
lt256
|
arxiv_abstracts
|
math/0302085
|
Let p be a prime and let F_pbar be the algebraic closure of the finite field
of p elements. Let f(x) be any one variable rational function over F_pbar with
n poles of orders d_1, ...,d_n. Suppose p is coprime to d_i for every i. We
prove that there exists a Hodge polygon, depending only on d_i's, which is a
lower bound to the Newton polygon of L functions of exponential sums of f(x).
Moreover, we show that these two polygons coincide if p=1 mod d_i for every
i=1,...,n. As a corollary, we obtain a tight lower bound of Newton polygon of
Artin-Schreier curve.
|
lt256
|
arxiv_abstracts
|
math/0302086
|
We give the description of the t-structure on the derived category of regular
holonomic D-modules corresponding to the trivial t-structure on the derived
category of constructible sheaves via Riemann-Hilbert correspondence. We give
also the condition for a decreasing sequence of families of supports to give a
t-structure on the derived category of coherent O-modules.
|
lt256
|
arxiv_abstracts
|
math/0302087
|
We announce a new proof of the uniform estimate on the curvature of solutions
to the Ricci flow on a compact K\"ahler manifold $M^n$ with positive
bisectional curvature. In contrast to the recent work of X. Chen and G. Tian,
our proof of the uniform estimate does not rely on the exsitence of
K\"ahler-Einstein metrics on $M^n$, but instead on the first author's Harnack
inequality for the K\"ahler-Ricc flow, and a very recent local injectivity
radius estimate of Perelman for the Ricci flow.
|
lt256
|
arxiv_abstracts
|
math/0302088
|
We apply ideas from conformal field theory to study symplectic
four-manifolds, by using modular functors to "linearise" Lefschetz fibrations.
In Chern-Simons theory this leads to the study of parabolic vector bundles of
conformal blocks. Motivated by the Hard Lefschetz theorem, we show the bundles
of SU(2) conformal blocks associated to Kaehler surfaces are Brill-Noether
special, although the associated flat connexions may be irreducible if the
surface is simply-connected and not spin.
|
lt256
|
arxiv_abstracts
|
math/0302089
|
A picture P of a graph G = (V,E) consists of a point P(v) for each vertex v
in V and a line P(e) for each edge e in E, all lying in the projective plane
over a field k and subject to containment conditions corresponding to incidence
in G. A graph variety is an algebraic set whose points parametrize pictures of
G. We consider three kinds of graph varieties: the picture space X(G) of all
pictures, the picture variety V(G), an irreducible component of X(G) of
dimension 2|V|, defined as the closure of the set of pictures on which all the
P(v) are distinct, and the slope variety S(G), obtained by forgetting all data
except the slopes of the lines P(e). We use combinatorial techniques (in
particular, the theory of combinatorial rigidity) to obtain the following
geometric and algebraic information on these varieties: (1) a description and
combinatorial interpretation of equations defining each variety
set-theoretically; (2) a description of the irreducible components of X(G); and
(3) a proof that V(G) and S(G) are Cohen-Macaulay when G satisfies a sparsity
condition, rigidity independence. In addition, our techniques yield a new proof
of the equality of two matroids studied in rigidity theory.
|
256
|
arxiv_abstracts
|
math/0302090
|
We show that coefficients in the Laurent series of Igusa Zeta functions are
periods. This will be used in a subsequent paper (by P. Brosnan) to show that
certain numbers occurring in study of Feynman amplitudes (upto gamma factors)
are periods.
|
lt256
|
arxiv_abstracts
|
math/0302091
|
Let A be a set of integers. For every integer n, let r_{A,h}(n) denote the
number of representations of n in the form n = a_1 + a_2 + ... + a_h, where
a_1, a_2,...,a_h are in A and a_1 \leq a_2 \leq ... \leq a_h. The function
r_{A,h}: Z \to N_0 \cup \infty is the representation function of order h for A.
The set A is called an asymptotic basis of order h if r_{A,h}^{-1}(0) is
finite, that is, if every integer with at most a finite number of exceptions
can be represented as the sum of exactly h not necessarily distinct elements of
A. It is proved that every function is a representation function, that is, if
f: Z \to N_0 \cup \infty is any function such that f^{-1}(0) is finite, then
there exists a set A of integers such that f(n) = r_{A,h}(n) for all n in Z.
Moreover, the set A can be arbitrarily sparse in the sense that, if \phi(x) \to
\infty, then there exists a set A with f(n) = r_{A,h}(n) such that card{a in A
: |a| \leq x} < \phi(x) for all sufficiently large x.
|
lt256
|
arxiv_abstracts
|
math/0302092
|
Using techniques developed in [Lasserre02], we show that some minimum
cardinality problems subject to linear inequalities can be represented as
finite sequences of semidefinite programs. In particular, we provide a
semidefinite representation of the minimum rank problem on positive
semidefinite matrices. We also use this technique to cast the problem of
finding convex lower bounds on the objective as a semidefinite program.
|
lt256
|
arxiv_abstracts
|
math/0302093
|
We describe a glueing construction for the Yang-Mills equations in dimension
$n > 4$. Our method is based on a construction of approximate solutions, and a
detailed analysis of the linearized operator near an approximate solution.
|
lt256
|
arxiv_abstracts
|
math/0302094
|
We describe a glueing construction for a certain self-dual reduction of the
Yang-Mills equations in dimension 8.
|
lt256
|
arxiv_abstracts
|
math/0302095
|
We study contraction groups for automorphisms of totally disconnected locally
compcat groups using the scale of the automorphism as a tool. The contraction
group is shown to be unbounded when the inverse automorphism has non-trivial
scale and this scale is shown to be the inverse value of the modular function
on the closure of the contraction group at the automorphism. The closure of the
contraction group is represented as acting on a homogenous tree and closed
contraction groups are characterised.
|
lt256
|
arxiv_abstracts
|
math/0302096
|
The use of bundle gerbes and bundle gerbe modules is considered as a
replacement for the usual theory of Clifford modules on manifolds that fail to
be spin. It is shown that both sides of the Atiyah-Singer index formula for
coupled Dirac operators can be given natural interpretations using this
language and that the resulting formula is still an identity.
|
lt256
|
arxiv_abstracts
|
math/0302097
|
Three examples of free field constructions for the vertex operators of the
elliptic quantum group ${\cal A}_{q,p}(\hat{sl}_2)$ are obtained. Two of these
(for $p^{1/2}=\pm q^{3/2},p^{1/2}=-q^2$) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
$Z$-algebra of Lepowsky and Wilson. The third one ($p^{1/2}=q^{3}$) is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at $p^{1/2}=q^{3}$, however, is not related to the deformed
Virasoro algebra. Using these free field constructions, an integral formula for
the correlation functions of Baxter's eight-vertex model is obtained. This
formula shows different structure compared with the one obtained by Lashkevich
and Pugai.
|
lt256
|
arxiv_abstracts
|
math/0302098
|
We show that several torsion free 3-manifold groups are not left-orderable.
Our examples are groups of cyclic branched covers of S^3 branched along links.
The figure eight knot provides simple nontrivial examples. The groups arising
in these examples are known as Fibonacci groups which we show not to be
left-orderable. Many other examples of non-orderable groups are obtained by
taking 3-fold branched covers of S^3 branched along various hyperbolic 2-bridge
knots. The manifold obtained in such a way from the 5_2 knot is of special
interest as it is conjectured to be the hyperbolic 3-manifold with the smallest
volume.
|
lt256
|
arxiv_abstracts
|
math/0302099
|
We introduce topological invariants of knots and braid conjugacy classes, in
the form of differential graded algebras, and present an explicit combinatorial
formulation for these invariants. The algebras conjecturally give the relative
contact homology of certain Legendrian tori in five-dimensional contact
manifolds. We present several computations and derive a relation between the
knot invariant and the determinant.
|
lt256
|
arxiv_abstracts
|
math/0302100
|
An equivariant version of the twisted inverse pseudofunctor is defined, and
equivariant versions of some important properties, including the Grothendieck
duality of proper morphisms and flat base change are proved. As an application,
a generalized version of Watanabe's theorem on the Gorenstein property of the
ring of invariants is proved.
|
lt256
|
arxiv_abstracts
|
math/0302101
|
In this article we discuss some numerical parts of the mirror conjecture. For
any 3 - dimensional Calabi - Yau manifold author introduces a generalization of
the Casson invariant known in 3 - dimensional geometry, which is called Casson
- Donaldson invariant. In the framework of the mirror relationship it
corresponds to the number of SpLag cycles which are Bohr - Sommerfeld with
respect to the given polarization. To compute the Casson - Donaldson invariant
the author uses well known in classical algebraic geometry degeneration
principle. By it, when the given Calabi - Yau manifold is deformed to a pair of
quasi Fano manifolds glued upon some K3 - surface, one can compute the
invariant in terms of "flag geometry" of the pairs (quasi Fano, K3 - surface).
|
lt256
|
arxiv_abstracts
|
math/0302102
|
Dyson a associe aux determinants de Fredholm des noyaux de Dirichlet pairs
(resp. impairs) une equation de Schrodinger sur un demi-axe et a employe les
methodes du scattering inverse de Gel'fand-Levitan et de Marchenko, en tandem,
pour etudier l'asymptotique de ces determinants. Nous avons propose suite a
notre mise-au-jour de l'operateur conducteur de chercher a realiser la
transformation de Fourier elle-meme comme un scattering, et nous obtenons ici
dans ce but deux systemes de Dirac sur l'axe reel tout entier et qui sont
associes intrinsequement, respectivement, aux transformations en cosinus et en
sinus.
(Dyson has associated with the Fredholm determinants of the even (resp. odd)
Dirichlet kernels a Schrodinger equation on the half-axis and has used, in
tandem, the Gel'fand-Levitan and Marchenko methods of inverse scattering theory
to study the asymptotics of these determinants. We have proposed following our
unearthing of the conductor operator to seek to realize the Fourier transform
itself as a scattering, and we obtain here to this end two Dirac systems on the
entire real axis which are intrinsically associated, respectively, to the
cosine and to the sine transforms.)
|
256
|
arxiv_abstracts
|
math/0302103
|
We consider the equations governing incompressible, viscous fluids in three
space dimensions, rotating around an inhomogeneous vector B(x): this is a
generalization of the usual rotating fluid model (where B is constant). We
prove the weak convergence of Leray--type solutions towards a vector field
which satisfies the usual 2D Navier--Stokes equation in the regions of space
where B is constant, with Dirichlet boundary conditions, and a heat--type
equation elsewhere. The method of proof uses weak compactness arguments.
|
lt256
|
arxiv_abstracts
|
math/0302104
|
This article examines arbitrage investment in a mispriced asset when the
mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained
investor maximizes a generalization of the Kelly criterion. The optimal
differentiable and threshold policies are derived. The optimal differentiable
policy is linear with respect to mispricing and risk-free in the long run. The
optimal threshold policy calls for investing immediately when the mispricing is
greater than zero with the investment amount inversely proportional to the risk
aversion parameter. The investment is risky even in the long run. The results
are consistent with the belief that credit-constrained arbitrageurs should be
risk-neutral if they are to engage in convergence trading.
|
lt256
|
arxiv_abstracts
|
math/0302105
|
We propose the first algebraic determinantal formula to enumerate tilings of
a centro-symmetric octagon of any size by rhombi. This result uses the
Gessel-Viennot technique and generalizes to any octagon a formula given by
Elnitsky in a special case.
|
lt256
|
arxiv_abstracts
|
math/0302106
|
Let $m_{12}$, $m_{13}$, ..., $m_{n-1,n}$ be the slopes of the $\binom{n}{2}$
lines connecting $n$ points in general position in the plane. The ideal $I_n$
of all algebraic relations among the $m_{ij}$ defines a configuration space
called the {\em slope variety of the complete graph}. We prove that $I_n$ is
reduced and Cohen-Macaulay, give an explicit Gr\"obner basis for it, and
compute its Hilbert series combinatorially. We proceed chiefly by studying the
associated Stanley-Reisner simplicial complex, which has an intricate recursive
structure. In addition, we are able to answer many questions about the geometry
of the slope variety by translating them into purely combinatorial problems
concerning enumeration of trees.
|
lt256
|
arxiv_abstracts
|
math/0302107
|
We provide new arguments to see topological Kac-Moody groups as generalized
semisimple groups over local fields: they are products of topologically simple
groups and their Iwahori subgroups are the normalizers of the pro-p Sylow
subgroups. We use a dynamical characterization of parabolic subgroups to prove
that some countable Kac-Moody groups with Fuchsian buildings are not linear. We
show for this that the linearity of a countable Kac-Moody group implies the
existence of a closed embedding of the corresponding topological group in a
non-Archimedean simple Lie group, thanks to a commensurator super-rigidity
theorem proved in the Appendix by P. Bonvin.
|
lt256
|
arxiv_abstracts
|
math/0302108
|
We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive
Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the condition of
the so called ``Ansatz'' can be dropped. That condition assumed that almost
every singular phase point had a hyperbolic trajectory after the singularity.
Having this condition dropped, the cited theorem becomes much stronger and
easier to apply. At the end of the paper two immediate corollaries of this
improvement are discussed: One of them is the (fully hyperbolic) Bernoulli
mixing property of every hard disk system (D=2), the other one claims that the
ergodic components of every hard ball system ($D\ge3$) are open.
|
lt256
|
arxiv_abstracts
|
math/0302109
|
Let $X\subset \P^n$ be a possibly singular hypersurface of degree $d\le n$,
defined over a finite field $k$. We show that the diagonal, suitably
interpreted, is decomposable. This gives a proof that the eigenvalues of the
Frobenius action on its $\ell$-adic cohomology $H^i(\bar{X}, \Q_\ell)$, for
$\ell \neq {\rm char}(k)$, are divisible by $q$, without using the result on
the existence of rational points by Ax and Katz.
|
lt256
|
arxiv_abstracts
|
math/0302110
|
Let G be a finite group and \rho: G--> End(E) be a group representation of G
on a coherent sheaf over an integral scheme. The purpose of this paper shall
give a decomposition theorem of such representations in non-splitting
components and apply this results to the studie of Galois covers
|
lt256
|
arxiv_abstracts
|
math/0302111
|
Let G be the group of rational points of a semisimple algebraic group of rank
1 over a nonarchimedean local field. We improve upon Lubotzky's analysis of
graphs of groups describing the action of lattices in G on its Bruhat-Tits tree
assuming a condition on unipotents in G. The condition holds for all but a few
types of rank 1 groups. A fairly straightforward simplification of Lubotzky's
definition of a cusp of a lattice is the key step to our results. We take the
opportunity to reprove Lubotzky's part in the analysis from this foundation.
|
lt256
|
arxiv_abstracts
|
math/0302112
|
We consider dimension reduction for solutions of the K\"ahler-Ricci flow with
nonegative bisectional curvature. When the complex dimension $n=2$, we prove an
optimal dimension reduction theorem for complete translating K\"ahler-Ricci
solitons with nonnegative bisectional curvature. We also prove a general
dimension reduction theorem for complete ancient solutions of the
K\"ahler-Ricci flow with nonnegative bisectional curvature on noncompact
complex manifolds under a finiteness assumption on the Chern number $c^n_1$.
|
lt256
|
arxiv_abstracts
|
math/0302113
|
We introduce and develop a language of semigroups over the braid groups for a
study of braid monodromy factorizations (bmf's) of plane algebraic curves and
other related objects. As an application we give a new proof of Orevkov's
theorem on realization of a bmf over a disc by algebraic curves and show that
the complexity of such a realization can not be bounded in terms of the types
of the factors of the bmf. Besides, we prove that the type of a bmf is
distinguishing Hurwitz curves with singularities of inseparable types up to
$H$-isotopy and $J$-holomorphic cuspidal curves in $\C P^2$ up to symplectic
isotopy.
|
lt256
|
arxiv_abstracts
|
math/0302114
|
We prove a summation formula for a bilateral series whose terms are products
of two basic hypergeometric functions. In special cases, series of this type
arise as matrix elements of quantum group representations.
|
lt256
|
arxiv_abstracts
|
math/0302115
|
We relate the formulas giving Brownian (and other) intersection exponents to
the absolute continuity relations between Bessel process of different
dimensions, via the two-parameter family of Schramm-Loewner Evolution processes
SLE(kappa,rho) introduced in arXiv:math.PR/0209343. This allows also to compute
the value of some new exponents (``hiding exponents'') related to SLEs and
planar Brownian motions.
|
lt256
|
arxiv_abstracts
|
math/0302116
|
In general the processes of taking a homotopy inverse limit of a diagram of
spectra and smashing spectra with a fixed space do not commute. In this paper
we investigate under what additional assumptions these two processes do
commute. In fact we deal with an equivariant generalization which involves
spectra and smash products over the orbit category of a discrete group. Such a
situation naturally occurs if one studies the equivariant homology theory
associated to topological cyclic homology. The main theorem of this paper will
play a role in the generalization of the results obtained by Boekstedt, Hsiang
and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map
for the family of virtually cyclic subgroups.
|
lt256
|
arxiv_abstracts
|
math/0302117
|
Let K be a number field and A an abelian variety over K. We are interested in
the following conjecture of Morita: if the Mumford-Tate group of A does not
contain unipotent Q-rational points then A has potentially good reduction at
any discrete place of K. The Mumford-Tate group is an object of analytical
nature whereas having good reduction is an arithmetical notion, linked to the
ramification of Galois representations. This conjecture has been proved by
Morita for particular abelian varieties with many endomorphisms (called of PEL
type). Noot obtained results for abelian varieties without non trivial
endomorphisms (Mumford's example, not of PEL type). We give new results for
abelian varieties not of PEL type.
|
lt256
|
arxiv_abstracts
|
math/0302118
|
We consider the topological entropy of state space and quasi-state space
homeomorphisms induced from C*-algebra automorphisms. Our main result asserts
that, for automorphisms of separable exact C*-algebras, zero Voiculescu-Brown
entropy implies zero topological entropy on the quasi-state space (and also
more generally on the entire unit ball of the dual). As an application we
obtain a simple description of the topological Pinsker algebra in terms of
local Voiculescu-Brown entropy.
|
lt256
|
arxiv_abstracts
|
math/0302119
|
The aim of this paper is to study harmonic polynomials on the quantum
Euclidean space E^N_q generated by elements x_i, i=1,2,...,N, on which the
quantum group SO_q(N) acts. The harmonic polynomials are defined as solutions
of the equation \Delta_q p=0, where p is a polynomial in x_i, i=1,2,...,N, and
the q-Laplace operator \Delta_q is determined in terms of the differential
operators on E^N_q. The projector H_m: {cal A}_m\to {\cal H}_{m} is
constructed, where {\cal A}_{m} and {\cal H}_m are the spaces of homogeneous of
degree m polynomials and homogeneous harmonic polynomials, respectively. By
using these projectors, a q-analogue of the classical zonal polynomials and
associated spherical polynomials with respect to the quantum subgroup SO_q(N-2)
are constructed. The associated spherical polynomials constitute an orthogonal
basis of {\cal H}_m. These polynomials are represented as products of
polynomials depending on q-radii and x_j, x_{j'}, j'=N-j+1. This representation
is in fact a q-analogue of the classical separation of variables. The dual pair
(U_q(sl_2), U_q(so_n)) is related to the action of SO_q(N) on E^N_q.
Decomposition into irreducible constituents of the representation of the
algebra U_q(sl_2)\times U_q(so_n) defined by the action of this algebra on the
space of all polynomials on E^N_q is given.
|
256
|
arxiv_abstracts
|
math/0302120
|
The holomorph of a discrete group $G$ is the universal semi-direct product of
$G$. In chapter 1 we describe why it is an interesting object and state main
results.
In chapter 2 we recall the classical definition of the holomorph as well as
this universal property, and give some group theoretic properties and examples
of holomorphs. In particular, we give a necessary and sufficient condition for
the existence of a map of split extensions for holomorphs of two groups.
In chapter 3 we construct a resolution for $Hol(Z_{p^r})$ for every prime
$p$, where ${\mathbb Z}_m$ denotes a cyclic group of order $m$, and use it to
compute the integer homology and mod $p$ cohomology ring of $Hol(Z_{p^r})$.
In chapter 4 we study the holomorph of the direct sum of several copies of
$Z_{p^r}$. We identify this holomorph as a nice subgroup of $GL(n+1, Z_{p^r})$,
thus its cohomology informs on the cohomology of the general linear group which
has been of interest in the subject. We show that the LHS spectral sequence for
$H^*(Hol(\bigoplus_n Z_{p^r}); F_p)$ does not collapse at the $E_2$ stage for
$p^r\ge 8$. Also, we compute mod $p$ cohomology and the first Bockstein
homomorphisms of the congruence subgroups given by $Ker (Hol(\bigoplus_n
Z_{p^r}) \to Hol(\bigoplus_n Z_p)).$
In chapter 5 we recall wreath products and permutative categories, and their
connections with holomorphs.
In chapter 6 we give a short proof of the well-known fact due to S. Eilenberg
and J. C. Moore that the only injective object in the category of groups is the
trivial group.
|
256
|
arxiv_abstracts
|
math/0302121
|
Combining the idea of motivic zeta function, due to Kapranov, and Pellikaan's
definition of a two- variable zeta function for curves over finite fields in
the present note we introduce a motivic two- variable zeta function for curves
over arbitrary fields and prove the generalizations of Pellikaan's results in
this context.
|
lt256
|
arxiv_abstracts
|
math/0302122
|
We use the DPW method to obtain the associate family of Delaunay surfaces and
derive a formula for the neck size of the surface in terms of the entries of
the holomorphic potential.
|
lt256
|
arxiv_abstracts
|
math/0302123
|
We consider a model of lattice gas dynamics in the d-dimensional cubic
lattice in the presence of disorder. If the particle interaction is only mutual
exclusion and if the disorder field is given by i.i.d. bounded random
variables, we prove the almost sure existence of the hydrodynamical limit in
dimension d>2. The limit equation is a non linear diffusion equation with
diffusion matrix characterized by a variational principle.
|
lt256
|
arxiv_abstracts
|
math/0302124
|
In this paper, we prove a global rigidity theorem for negatively curved
Finsler metrics on a compact manifold of dimension n>2. We show that for such a
Finsler manifold, if the flag curvature is a scalar function on the tangent
bundle, then the Finsler metric is of Randers type. We also study the case when
the Finsler metric is locally projectively flat.
|
lt256
|
arxiv_abstracts
|
math/0302125
|
In this paper we prove, assuming the Generalised Riemann Hypothesis, a
conjecture of Yves Andre that that asserts that a curve in a Shimura variety
containing an infinite set of special points is of Hodge type.
|
lt256
|
arxiv_abstracts
|
math/0302126
|
For any finite set $\A$ of $n$ points in $\R^2$, we define a
$(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the
poset of ``non-crossing marked graphs'' with vertex set $\A$, where a marked
graph is defined as a geometric graph together with a subset of its vertices.
The poset of non-crossing graphs on $\A$ appears as the complement of the star
of a face in that polyhedron.
The polyhedron has a unique maximal bounded face, of dimension $2n_i +n -3$
where $n_i$ is the number of points of $\A$ in the interior of $\conv(\A)$. The
vertices of this polytope are all the pseudo-triangulations of $\A$, and the
edges are flips of two types: the traditional diagonal flips (in
pseudo-triangulations) and the removal or insertion of a single edge.
As a by-product of our construction we prove that all pseudo-triangulations
are infinitesimally rigid graphs.
|
lt256
|
arxiv_abstracts
|
math/0302127
|
For nonsmooth Euler-Lagrange extremals, Noether's conservation laws cease to
be valid. We show that Emmy Noether's theorem of the calculus of variations is
still valid in the wider class of Lipschitz functions, as long as one restrict
the Euler-Lagrange extremals to those which satisfy the DuBois-Reymond
necessary condition. In the smooth case all Euler-Lagrange extremals are
DuBois-Reymond extremals, and the result gives a proper extension of the
classical Noether's theorem. This is in contrast with the recent developments
of Noether's symmetry theorems to the optimal control setting, which give rise
to non-proper extensions when specified for the problems of the calculus of
variations.
|
lt256
|
arxiv_abstracts
|
math/0302128
|
We describe a variant of K-theory for spaces with involution, built from
vector bundles which are sent to their negative under the involution.
|
lt256
|
arxiv_abstracts
|
math/0302129
|
We study a dissipative nonlinear equation modelling certain features of the
Navier-Stokes equations. We prove that the evolution of radially symmetric
compactly supported initial data does not lead to singularities in dimensions
$n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting
existence of blow-up solutions. Moreover, using the same techniques we
numerically confirm a conjecture of Lepin regarding existence of self-similar
singular solutions to a semi-linear heat equation.
|
lt256
|
arxiv_abstracts
|
math/0302130
|
We classify module categories over the category of representations of quantum
$SL(2)$ in a case when $q$ is not a root of unity. In a case when $q$ is a root
of unity we classify module categories over the semisimple subquotient of the
same category.
|
lt256
|
arxiv_abstracts
|
math/0302131
|
This is the first in a series of papers exploring the relationship between
the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of
a 3-manifold with the integral homology of a torus, given by counting
projectively flat connections. We show that its mod 2 evaluation is given by
the triple cup product in cohomology, and so it coincides with a sum of Rohlin
invariants. Our counting argument makes use of a natural action of the first
cohomology on the moduli space of projectively flat connections; along the way
we construct perturbations that are equivariant with respect to this action.
Combined with the Floer exact triangle, this gives a purely gauge-theoretic
proof that Casson's homology sphere invariant reduces mod 2 to the Rohlin
invariant.
|
lt256
|
arxiv_abstracts
|
math/0302132
|
The paper describes a method to determine symmetrized weight enumerators of
$p^m$-linear codes based on the notion of a disjoint weight enumerator.
Symmetrized weight enumerators are given for the lifted quadratic residue codes
of length 24 modulo $2^m$ and modulo $3^m$, for any positive $m$.
|
lt256
|
arxiv_abstracts
|
math/0302133
|
Let C be a smooth complex projective curve of genus at least 2 and let M be
the moduli space of rank 2, stable vector bundles on C, with fixed determinant
of degree 1. For any k>1, we find two irreducible components of the space of
rational curves of degree k on M. One component, which we call the nice
component has the property that the general element is a very free curve if k
is sufficiently large. The other component has the general element a free
curve. Both components have the expected dimension and their maximal rationally
connected fibration is the Jacobian of the curve C.
|
lt256
|
arxiv_abstracts
|
math/0302134
|
For the implicit systems of first order ordinary differential equations on
the plane there is presented the complete local classification of generic
singularities of family of its phase curves up to smooth orbital equivalence.
Besides the well known singularities of generic vector fields on the plane and
the singularities described by a generic first order implicit differential
equations, there exists only one generic singularity described by the implicit
first order equation supplied by Whitney umbrella surface generically embedded
to the space of directions on the plane.
|
lt256
|
arxiv_abstracts
|
math/0302135
|
This is a continuation of "Rational families of vector bundles on curves, I".
Let C be a smooth projective curve of genus at least 2 and let M be the moduli
space of rank 2, stable vector bundles on C, with fixed determinant of degree
1. For any k>0, we find all the irreducible components of the space of rational
curves of degree k on M and their maximal rationally connected quotients.
|
lt256
|
arxiv_abstracts
|
math/0302136
|
Let $W$ be a finite Weyl group of classical type which may not be
irreducible, $F$ an algebraically closed field, $q$ an invertible element of
$F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then
it is $FW$ and we know the representation type. Thus, we assume that $q\ne 1$.
Let $P_W(x)$ be the Poincare polynomial of $W$. It is well-known that $\mathcal
H_W(q)$ is semisimple if and only if $x-q$ does not divide $P_W(x)$. We show
that the similar results hold for finiteness, tameness and wildness. In other
words, the Poincare polynomial governs the representation type of $\mathcal
H_W(q)$ completely. Note that the finiteness result was already given in the
author's previous papers, some of which were written with Andrew Mathas.
The proof uses the Fock space theory, which was developed for proving the LLT
conjecture (see AMS Univ. Lec. Ser. 26), the Specht module theory, which was
developed by Dipper, James and Murphy in this case, and results from the theory
of finite dimensional algebras.
|
256
|
arxiv_abstracts
|
math/0302137
|
In order to obtain solutions to problem $$ {{array}{c} -\Delta
u=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0
\hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}.
$$ $h$ and $k$ must be chosen taking into account not only the size of some
norm but the shape. Moreover, if $h(x)\equiv 0$, to reach multiplicity of
solution, some hypotheses about the local behaviour of $k$ close to the points
of maximum are needed.
|
lt256
|
arxiv_abstracts
|
math/0302138
|
We prove the Andre-Oort conjecture on special points of Shimura varieties for
arbitrary products of modular curves, assuming the Generalized Riemann
Hypothesis. More explicitly, this means the following. Let n be a positive
integer, and let S be a subset of C^n (with C the complex numbers) consisting
of points all of whose coordinates are j-invariants of elliptic curves with
complex multiplications. Then we prove (under GRH) that the irreducible
components of the Zariski closure of S are ``special subvarieties'', i.e.,
determined by isogeny conditions on coordinates and pairs of coordinates. A
weaker variant is proved unconditionally.
|
lt256
|
arxiv_abstracts
|
math/0302139
|
We construct a finite 1-connected CW complex X such that $H_*(\Omega X; Z)$
has p-torsion for the infinitely many primes satisfying p ~ 5,7,17,19 mod 24,
but no p-torsion for the infinitely many primes satisfying p ~ 13 or 23 mod 24.
|
lt256
|
arxiv_abstracts
|
math/0302140
|
If A is a graded connected algebra then we define a new invariant, polydepth
A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most
polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite
category, and if the orbits of H_*(\Omega Y) acting in the homology of the
homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite
polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite
then either L is solvable and UL grows at most polynomially or else for some
integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some
$k(r)$.
|
lt256
|
arxiv_abstracts
|
math/0302141
|
Given a pair of dynamical systems we consider a pair of commuting von Neumann
factors of type 11_1. The construction is a generalization of classical von
Neumann-Murrey and grouppoid construction. It gives a natural examples of
factors with non-unit coupling constant.As the partial cases we obtain
Connes-Riffel-Faddeev examples of the representations of rotation algebra. We
give also an example for infinite symmetric group.
|
lt256
|
arxiv_abstracts
|
math/0302142
|
We revisit the ladder operators for orthogonal polynomials and re-interpret
two supplementary conditions as compatibility conditions of two linear
over-determined systems; one involves the variation of the polynomials with
respect to the variable z (spectral parameter) and the other a recurrence
relation in n (the lattice variable). For the Jacobi weight w(x) =
(1-x)^a(1+x)^b, x in [-1,1],we show how to use the compatibility conditions to
explicitly determine the recurrence coefficients of the monic Jacobi
polynomials.
|
lt256
|
arxiv_abstracts
|
math/0302143
|
In a recent paper, Dimca and Nemethi pose the problem of finding a
homogeneous polynomial f such that the homology of the complement of the
hypersurface defined by f is torsion-free, but the homology of the Milnor fiber
of f has torsion. We prove that this is indeed possible, and show by
construction that, for each prime p, there is a polynomial with p-torsion in
the homology of the Milnor fiber. The techniques make use of properties of
characteristic varieties of hyperplane arrangements.
|
lt256
|
arxiv_abstracts
|
math/0302144
|
We prove lower bounds on $||T_t||$, where $T_t$ is a one-parameter semigroup,
starting from information on the resolvent norms, i.e. the pseudospectra. We
provide a physically important example in which the growth of the semigroup
norm cannot be derived from spectral information. The generator is a
self-adjoint Schr\"odinger operator, but the semigroup growth is measured using
the $L^1$ norm rather than the $L^2$ norm. Numerical confirmation of the
results is provided.
|
lt256
|
arxiv_abstracts
|
math/0302145
|
We discuss the problems arising when computing eigenvalues of self-adjoint
operators which lie in a gap between two parts of the essential spectrum.
Spectral pollution, i.e. the apparent existence of eigenvalues in numerical
computations, when no such eigenvalues actually exist, is commonplace in
problems arising in applied mathematics. We describe a geometrically inspired
method which avoids this difficulty, and show that it yields the same results
as an algorithm of Zimmermann and Mertins.
|
lt256
|
arxiv_abstracts
|
math/0302146
|
We define an analog of the Poisson integral formula for a family of the
non-commutative Lobachevsky spaces. The $q$-Fourier transform of the Poisson
kernel is expressed through the $q$-Bessel-Macdonald function.
|
lt256
|
arxiv_abstracts
|
math/0302147
|
Let N_q(g) the maximal number of points on a genus g curve over F_q. We prove
that N_3(5)=13.
|
lt256
|
arxiv_abstracts
|
math/0302148
|
We present several formulae for the Selberg type integrals associated with
the Lie algebra $sl_3$.
|
lt256
|
arxiv_abstracts
|
math/0302149
|
In this article, we calculate the period determinant of an irrgular singular
connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate
its de Rham cohomology and the cycles in the homology of the dual connection
and describe the period matrix. Terasoma's work is introduced to approximate
the direct image connection pi_*(\nabla) by a sequence of regular connections
as an intermediate step where pi:U -> A^1(y), (x,y) |-> y. Finally, we will
compare the period obtained by this approximation of the direct image
connection and the original.
|
lt256
|
arxiv_abstracts
|
math/0302150
|
By applying the symplectic cutting operation to cotangent bundles, one can
construct a large number of interesting symplectic cones. In this paper we show
how to attach algebras of pseudodifferential operators to such cones and
describe the symbolic properties of the algebras.
|
lt256
|
arxiv_abstracts
|
math/0302151
|
We study a class of perverse sheaves on the variety of pairs (P,gU_P) where P
runs through a conjugacy class of parabolics in a connected reductive group G
and gU_P runs through G/U_P. This is a generalization of the theory of
character sheaves.
|
lt256
|
arxiv_abstracts
|
math/0302152
|
We survey some recent results and constructions of almost-K\"ahler manifolds
whose curvature tensors have certain algebraic symmetries. This is an updated
and corrected version of the (to be) published manuscript.
|
lt256
|
arxiv_abstracts
|
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