Hodge-Theoretic Mirror Symmetry for Toric Stacks

Tom Coates Imperial College London Alessio Corti Imperial College London Hiroshi Iritani Kyoto University Hsian-Hua Tseng Ohio State University

Algebraic Geometry mathscidoc:1801.01001

Distinguished Paper Award in 2020

Journal of Differential Geometry, 114, (1), 41-115, 2020.1
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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  title={Hodge-Theoretic Mirror Symmetry for Toric Stacks},
  author={Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng},
  booktitle={Journal of Differential Geometry},
Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng. Hodge-Theoretic Mirror Symmetry for Toric Stacks. 2020. Vol. 114. In Journal of Differential Geometry. pp.41-115. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180104231716194696866.
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