### 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, 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.

Original language | English (US) |
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Pages (from-to) | 145-174 |

Number of pages | 30 |

Journal | Communications in Mathematical Physics |

Volume | 296 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2010 |

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## Cite this

*Communications in Mathematical Physics*,

*296*(1), 145-174. https://doi.org/10.1007/s00220-009-0929-7