# 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={R. P. Horja}, journal={arXiv: Algebraic Geometry}, year={2012} }

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…

## One Citation

Applications of homological mirror symmetry to hypergeometric systems: duality conjectures

- Mathematics, Physics
- 2013

Homological mirror symmetry for crepant resolutions of Gorenstein toric singularities leads to a pair of conjectures on certain hypergeometric systems of PDEs. We explain these conjectures and verify…

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