FJRW rings and Landau-Ginzburg Mirror Symmetry

Abstract

In this article, we study the Berglund--Hübsch transpose construction W^T for invertible quasihomogeneous potential W. We introduce the dual group G^T and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten A-model of W/G and the orbifold Milnor ring B-model of W^T/G^T. Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G^max. Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual W^SD.

32 pages

References in corpus (1)

• FJRW-Rings and Landau-Ginzburg Mirror Symmetry in Two Dimensions

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• Monodromy of dual invertible polynomials
• From primitive form to mirror symmetry
• Hyperplane sections and stable derived categories
• General Mirror Pairs for Gauged Linear Sigma Models
• A note on bimodal singularities and mirror symmetry