FJRW rings and Landau-Ginzburg Mirror Symmetry

Details FJRW rings and Landau-Ginzburg Mirror Symmetry FJRW rings and Landau-Ginzburg Mirror Symmetry

2009-06-04

arxiv.org/abs/0906.0796v1

Mathematics

Algebraic Geometry

32 pages

Scientific paper

In this article, we study the Berglund--H\"ubsch 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.

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