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Article Dans Une Revue Duke Mathematical Journal Année : 2016

A Landau–Ginzburg mirror theorem without concavity

Résumé

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.

Dates et versions

hal-01555035 , version 1 (03-07-2017)

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Citer

Jérémy Guéré. A Landau–Ginzburg mirror theorem without concavity. Duke Mathematical Journal, 2016, 165 (13), pp.2461-2527. ⟨10.1215/00127094-3477235⟩. ⟨hal-01555035⟩
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