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

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

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

References in corpus (2)

• On the $K$-theory of smooth toric DM stacks
• String Cohomology of a Toroidal Singularity