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.
Citation
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
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