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arXiv · 1307.5070

A Landau--Ginzburg mirror theorem without concavity

Jérémy Guéré
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Abstract

We provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave 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. 2013-07-18. A Landau--Ginzburg mirror theorem without concavity. https://doi.org/10.1215/00127094-3477235

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