FJRW-rings and mirror symmetry

Marc Krawitz, Nathan Priddis, Pedro Acosta, Natalie Bergin, Himal Rathnakumara

Research output: Contribution to journalArticle

11 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)145-174
Number of pages30
JournalCommunications in Mathematical Physics
Volume296
Issue number1
DOIs
StatePublished - Mar 1 2010

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    Krawitz, M., Priddis, N., Acosta, P., Bergin, N., & Rathnakumara, H. (2010). FJRW-rings and mirror symmetry. Communications in Mathematical Physics, 296(1), 145-174. https://doi.org/10.1007/s00220-009-0929-7