相关论文: GKZ Hypergeometric Structures

We present a detailed analysis of the GKZ(Gel'fand, Kapranov and Zelevinski) hypergeometric systems in the context of mirror symmetry of Calabi-Yau hypersurfaces in toric varieties. As an application we will derive a concise formula for the…

We analyze GKZ(Gel'fand, Kapranov and Zelevinski) hypergeometric systems and apply them to study the quantum cohomology rings of Calabi-Yau manifolds. We will relate properties of the local solutions near the large radius limit to the…

The Gamma-series of Gel'fand-Kapranov-Zelevinsky are adapted so that they give solutions for certain resonant systems of GKZ hypergeometric differential equations. For this some complex parameters in the Gamma-series are replaced by…

We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of…

We review some classical and modern aspects of hypergeometric differential equations, including $A$-hypergeometric systems of Gel'fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler-Koszul homology, rank…

We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop…

This paper presents some parallel developments in Quiver/Dimer Models, Hypergeometric Systems and Dessins d'Enfants. The setting in which Gelfand, Kapranov and Zelevinsky have formulated the theory of hypergeometric systems, provides also a…

A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration $A \subset \mathbb{R}^d$ a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular…

To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the…

This paper deals with some analytic aspects of GG system introduced by I.M.Gelfand and M.I.Graev: we compute the dimension of the solution space of GG system over the field of functions meromorphic and periodic with respect to a lattice. We…

We investigate the GKZ $A$-hypergeometric $\mathscr{D}$-modules, introduced by Gel'fand, Kapranov, and Zelevinskii, arising from cyclic covers of toric varieties and find its Riemann--Hilbert partner. This extends our earlier results in…

We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kemp\'e de F\'eriet's hypergeometric series, and study the system of differential equations that it satisfies. We determine the…

Although this article can be read independently, it is a continuation of the introduction to integrable systems aspects of quantum cohomology given in part 1 (math.DG/0104274). In the same elementary style, i.e. assuming basic properties of…

We apply the better-behaved GKZ hypergeometric systems to study toric Calabi-Yau Deligne-Mumford stacks and their Hori-Vafa mirrors given by affine hypersurfaces in algebraic tori. We show that the integral structures of A-branes and…

These are the lecture notes from the 26th Winter School "Geometry and Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent…

This is the author's Habilitation which took place at University of Essen on July 11, 1993. The manuscript contains two parts. The first one is devoted to the author's combinatorial construction of mirrors of Calabi-Yau hypersurfaces in…

This is an introduction to the hyperderminant, according to Gelfand, Kapranov and Zelevinsky. The "triangle inequality", characterizing the Segre varieties such that their dual variety is a hypersurface, is proved in a geometric way…

For a finite set A of integral vectors, Gel'fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a D-module, which system is called an A-hypergeometric (or a GKZ hypergeometric) system.…

In these two lectures, delivered at the XXXVII Karpacz Winter School, February 2001, I review some applications of superspace in various topics related to string theory and M-theory. The first lecture is mainly devoted to descriptions of…

The paper presents a construction of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{g}_2$. The representation space is constructed as the space of solutions to a certain system of partial differential equations…