FJRW-rings and mirror symmetry

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

doi:10.1007/s00220-009-0929-7

FJRW-rings and mirror symmetry

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

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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)
Pages (from-to)	145-174
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	296
Issue number	1
DOIs	https://doi.org/10.1007/s00220-009-0929-7
State	Published - Mar 2010
Externally published	Yes

Bibliographical note

Funding Information:
M. K. is partially Supported by the National Research Foundation of South Africa.

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AU - Krawitz, Marc

AU - Priddis, Nathan

AU - Acosta, Pedro

AU - Bergin, Natalie

AU - Rathnakumara, Himal

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AB - 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.

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FJRW-rings and mirror symmetry

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