相关论文: Bivariate hypergeometric D-modules
The great success of the theory of hypergeometric series in one variable has stimulated the development of a corresponding theory in two and more variables. Horn has investigated the convergence of 34 (14 complete and 20 confluent)…
A function that is analytic on a domain of $\mathbb{C}^n$ is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein-Sato polynomial…
For finite complex reflexion groups, we consider the graded $W$-modules of diagonally harmonic polynomials in $r$ sets of variables, and show that associated Hilbert series may be described in a global manner, independent of the value of…
We develop a theory of principal determinants and hypergeometric systems for realizable matroids. Our framework parallels the toric theory of Gel'fand, Kapranov, and Zelevinsky (GKZ), but with the combinatorics of matroids and their flats…
By a codimension-one system we mean a system whose lattice of relations has rank one. We consider codimension-one $A$-hypergeometric systems and explicitly construct some of the logarithmic series solutions at the origin. When the parameter…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
In this paper, we consider the generalized isomonodromic deformations of rank two irregular connections on the Riemann sphere. We introduce Darboux coordinates on the parameter space of a family of rank two irregular connections by apparent…
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include:…
We prove a generalised version of finiteness of skein modules for 3-manifolds by including boundary. We show that internal skein modules are holonomic modules over the internal skein algebra of the boundary - a property including finite…
The aim of this note is a combinatorial description of a category of $D$-modules over an affine space, smooth along the stratification defined by an arrangement of hyperplanes. These $D$-modules are assumed to satisfy certain non-resonance…
We consider logarithmic vector fields parametrized by finite collections of weighted hyperplanes. For a finite collection of weighted hyperplanes in a two-dimensional vector space, it is known that the set of such vector fields is a free…
We establish some connections between nonresonant $A$-hypergeometric systems and de Rham-type complexes. This allows us to determine which of these $A$-hypergeometric systems "come from geometry."
Roughly speaking, holonomic measures are parametric varifolds without boundary. They provide a setting appropriate for the analysis of many variational problems. In this paper, we characterize the space of variations for these objects, and…
In this paper we introduce the notion of D-valued 2-norm on hy- perbolic or D-valued modules. Further, we define D-linear 2-functional on these modules and consider some of their properties. We also establish the Hahn- Banach type extension…
Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle…
We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta )$ via the explicit construction of Gevrey series solutions along coordinate subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along coordinate…