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15 September 2016 A Landau–Ginzburg mirror theorem without concavity
Jérémy Guéré
Duke Math. J. 165(13): 2461-2527 (15 September 2016). DOI: 10.1215/00127094-3477235

Abstract

We provide a mirror symmetry theorem in a range of cases where state-of-the-art techniques that rely on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials (named for the Fan, Jarvis, Ruan, and Witten quantum singularity theory) which is viewed as the counterpart of a nonconvex Gromov–Witten potential via the physical Landau–Ginzburg/Calabi–Yau (LG/CY) correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob’s virtual cycle in genus zero. In the nonconcave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the FJRW virtual cycle and a proof of mirror symmetry for FJRW theory.

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Jérémy Guéré. "A Landau–Ginzburg mirror theorem without concavity." Duke Math. J. 165 (13) 2461 - 2527, 15 September 2016. https://doi.org/10.1215/00127094-3477235

Information

Received: 1 December 2013; Revised: 1 October 2015; Published: 15 September 2016
First available in Project Euclid: 12 May 2016

zbMATH: 1354.14081
MathSciNet: MR3546967
Digital Object Identifier: 10.1215/00127094-3477235

Subjects:
Primary: 14N35
Secondary: 14J33

Keywords: chain polynomial , FJRW theory , Givental’s formalism , invertible polynomial , J-function , LG model , matrix factorization , mirror symmetry , nonconcavity , non-concavity , quantum product , recursive complex , spin curves , virtual cycle

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 13 • 15 September 2016
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