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

R. Paul Horja

doi:10.1142/9789814412551_0016

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

Algebraic Geometry 2017-08-23 v1 High Energy Physics - Theory

Authors: R. Paul Horja

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Abstract

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 $\beta \in N \otimes {\mathbb C}.$

Keywords

toric Deligne-Mumford stacks orbifold cohomology Grothendieck ring stacky fan GKZ hypergeometric system mirror symmetry Gamma-series solutions

Cite

@article{arxiv.1205.0025,
  title  = {Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system},
  author = {R. Paul Horja},
  journal= {arXiv preprint arXiv:1205.0025},
  year   = {2017}
}

Comments

LaTex, 19 pages; submitted as a contribution to the volume "Strings, Gauge Fields, and the Geometry Behind - The Legacy of Maximilian Kreuzer"

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

Abstract

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