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Landau-Ginzburg mirror symmetry conjecture. (English) Zbl 1509.14079

Summary: We prove the Landau-Ginzburg mirror symmetry conjecture between invertible quasihomogeneous polynomial singularities at all genera. That is, we show that the FJRW theory (LG A-model) of such a polynomial is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial.

MSC:

14J33 Mirror symmetry (algebro-geometric aspects)
14B05 Singularities in algebraic geometry
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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