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FJRW-Rings and Mirror Symmetry

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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 \({\fancyscript{H}_{W,G}}\) 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.

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References

  1. Arnol’d, V., Gusein-Zade, S., Varchenko, A.: Singularities of Differentiable Maps Vols I, II. Basel-Boston: Birkhauser, 1985

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  3. Fan, H., Jarvis, T.J., Ruan, Y.: The witten equation, mirror symmetry and quantum singularity theory. http://arxiv.org/abs/:0712.4021v3[math.AG], 2009

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Marc Krawitz

  2. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Nathan Priddis, Pedro Acosta, Natalie Bergin & Himal Rathnakumara

Authors
  1. Marc Krawitz
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  2. Nathan Priddis
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  3. Pedro Acosta
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  4. Natalie Bergin
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  5. Himal Rathnakumara
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Corresponding author

Correspondence to Nathan Priddis.

Additional information

Communicated by A. Kapustin

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

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Krawitz, M., Priddis, N., Acosta, P. et al. FJRW-Rings and Mirror Symmetry. Commun. Math. Phys. 296, 145–174 (2010). https://doi.org/10.1007/s00220-009-0929-7

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  • DOI: https://doi.org/10.1007/s00220-009-0929-7

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