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January 2020 Hodge-theoretic mirror symmetry for toric stacks
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
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J. Differential Geom. 114(1): 41-115 (January 2020). DOI: 10.4310/jdg/1577502022

Abstract

Using the mirror theorem [15], 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 Gelfand–Kapranov–Zelevinsky (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. "Hodge-theoretic mirror symmetry for toric stacks." J. Differential Geom. 114 (1) 41 - 115, January 2020. https://doi.org/10.4310/jdg/1577502022

Information

Received: 16 October 2016; Published: January 2020
First available in Project Euclid: 28 December 2019

zbMATH: 07147343
MathSciNet: MR4047552
Digital Object Identifier: 10.4310/jdg/1577502022

Rights: Copyright © 2020 Lehigh University

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Vol.114 • No. 1 • January 2020
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