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 WT such that the orbifold A-model of W/G is isomorphic to the B-model of WT. The Landau-Ginzburg A-model is the Frobenius algebra, HW,G constructed by Fan, Jarvis, and Ruan, and the B-model is the orbifold Milnor ring of WT. 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.
Bibliographical noteFunding Information:
M. K. is partially Supported by the National Research Foundation of South Africa.