Abstract
The Landau-Ginzburg Mirror Symmetry Conjecture states that for an invertible quasi-homogeneous singularity W and its maximal group G of diagonal symmetries, there is a dual singularity W T such that the orbifold A-model of W/G is isomorphic to the B-model of W T. The Landau-Ginzburg A-model is the Frobenius algebra \({\fancyscript{H}_{W,G}}\) constructed by Fan, Jarvis, and Ruan, and the B-model is the orbifold Milnor ring of W T. We verify the Landau-Ginzburg Mirror Symmetry Conjecture for Arnol’d’s list of unimodal and bimodal quasi-homogeneous singularities with G the maximal diagonal symmetry group, and include a discussion of eight axioms which facilitate the computation of FJRW-rings.
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Fan, H., Jarvis, T.J., Ruan, Y.: The witten equation, mirror symmetry and quantum singularity theory. http://arxiv.org/abs/:0712.4021v3[math.AG], 2009
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Communicated by A. Kapustin
M. K. is partially Supported by the National Research Foundation of South Africa.
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Krawitz, M., Priddis, N., Acosta, P. et al. FJRW-Rings and Mirror Symmetry. Commun. Math. Phys. 296, 145–174 (2010). https://doi.org/10.1007/s00220-009-0929-7
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DOI: https://doi.org/10.1007/s00220-009-0929-7