# 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 $\beta \in N \otimes {\mathbb C… 1 Citations ## References SHOWING 1-10 OF 13 REFERENCES The orbifold Chow ring of toric Deligne-Mumford stacks • Mathematics • 2004 Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a On the better behaved version of the GKZ hypergeometric system • Mathematics • 2010 We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated On the$K$-theory of smooth toric DM stacks • Mathematics • 2005 We explicitly calculate the Grothendieck$K$-theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate$K$-theory pushforwards and Homological methods for hypergeometric families • Mathematics • 2004 We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we String Cohomology of a Toroidal Singularity We construct explicitly regular sequences in the semigroup ring$R=\CC[K]$of lattice points of the graded cone$K$. We conjecture that the quotients of$R\$ by these sequences describe locally
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Horja, On the better behaved version of the GKZ hypergeometric system, preprint
• 2010