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arXiv · 1405.4530

Mirror symmetry for exceptional unimodular singularities

Changzheng Li·Si Li·Kyoji Saito·Yefeng Shen
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Abstract

In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on Landau-Ginzburg A-side. On the B-side, we compute the genus-zero generating function from a perturbative formula of primitive forms introduced by the first three authors recently. This computation matches the orbifold-Grothendieck-Riemann-Roch and WDVV calculations in FJRW theory on the A-side. The coincidence of the full data at all genera is established by reconstruction techniques. Our result establishes the first examples of LG-LG mirror symmetry of all genera for weighted homogeneous polynomials of central charge greater than one (i.e. which contain negative degree deformation parameters).

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Changzheng Li, Si Li, Kyoji Saito, Yefeng Shen. 2014-05-18. Mirror symmetry for exceptional unimodular singularities. https://arxiv.org/abs/1405.4530

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