Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system

@article{Horja2012ToricDS,
  title={Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system},
  author={Richard Paul Horja},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
  • R. P. Horja
  • Published 30 April 2012
  • Mathematics
  • arXiv: Algebraic Geometry
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the presence of a deformation parameter $\beta \in N \otimes {\mathbb C}.$ As an application, we construct a topological mirror symmetry map that produces a complete system of $\Gamma$--series solutions to the better behaved version of the GKZ hypergeometric system for $\beta \in N \otimes {\mathbb C… 
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Applications of homological mirror symmetry to hypergeometric systems: duality conjectures

References

SHOWING 1-10 OF 13 REFERENCES
Mellin-Barnes integrals as Fourier-Mukai transforms
The orbifold Chow ring of toric Deligne-Mumford stacks
Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a…
On the better behaved version of the GKZ hypergeometric system
We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated…
On the $K$-theory of smooth toric DM stacks
We explicitly calculate the Grothendieck $K$-theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate $K$-theory pushforwards and…
Homological methods for hypergeometric families
We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we…
String Cohomology of a Toroidal Singularity
We construct explicitly regular sequences in the semigroup ring $R=\CC[K]$ of lattice points of the graded cone $K$. We conjecture that the quotients of $R$ by these sequences describe locally…
Maximal Degeneracy Points of GKZ Systems
Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel'fand-Kapranov-Zelevinsky(GKZ) hypergeometric system. Some of these solutions arise as period integrals…
Resonant Hypergeometric Systems and Mirror Symmetry
In Part I the Γ-series of [11] are adapted so that they give solutions for certain resonant systems of Gel’fand-Kapranov-Zelevinsky hypergeometric differential equations. For this some complex…
Grbner Deformations of Hypergeometric Differential Equations
The theory of Grbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Grbner bases from the point of view of geometric deformations. The…
Hypergeometric functions and toric varieties
  • (Russian) Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 12–26; translation in Funct. Anal. Appl. 23
  • 1989
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