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arXiv · 1606.07254

Hodge-Theoretic Mirror Symmetry for Toric Stacks

Tom Coates·Alessio Corti·Hiroshi Iritani·Hsian-Hua Tseng
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Abstract

Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric Deligne-Mumford stack is isomorphic to the Saito structure associated to the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the quantum D-module, and a combinatorial description of quantum cohomology as a quantum Stanley-Reisner ring. We establish the convergence of the mirror isomorphism and of quantum cohomology in the big and equivariant setting.

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Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng. 2016-06-23. Hodge-Theoretic Mirror Symmetry for Toric Stacks. https://doi.org/10.4310/jdg%2F1577502022

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