Mirror symmetry for exceptional unimodular singularities
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).
Cite
@article{arxiv.1405.4530,
title = {Mirror symmetry for exceptional unimodular singularities},
author = {Changzheng Li and Si Li and Kyoji Saito and Yefeng Shen},
journal= {arXiv preprint arXiv:1405.4530},
year = {2014}
}
Comments
A proof of Proposition 2.7 is added. Some minor mistakes corrected. To appear in J. Eur. Math. Soc