Lattices for Landau-Ginzburg orbifolds

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Authors

  • Wolfgang Ebeling
  • Atsushi Takahashi

Research Organisations

External Research Organisations

  • Osaka University
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Details

Original languageEnglish
Pages (from-to)639-659
Number of pages21
JournalMathematische Zeitschrift
Volume296
Issue number1-2
Early online date5 Dec 2019
Publication statusPublished - Oct 2020

Abstract

We consider a pair consisting of an invertible polynomial and a finite abelian group of its symmetries. Berglund, Hübsch, and Henningson proposed a duality between such pairs giving rise to mirror symmetry. We define an orbifoldized signature for such a pair using the orbifoldized elliptic genus. In the case of three variables and based on the homological mirror symmetry picture, we introduce two integral lattices, a transcendental and an algebraic one. We show that these lattices have the same rank and that the signature of the transcendental one is the orbifoldized signature. Finally, we give some evidence that these lattices are interchanged under the duality of pairs.

Cite this

Lattices for Landau-Ginzburg orbifolds. / Ebeling, Wolfgang; Takahashi, Atsushi.
In: Mathematische Zeitschrift, Vol. 296, No. 1-2, 10.2020, p. 639-659.

Research output: Contribution to journal › Article › Research › peer review

Ebeling, W & Takahashi, A 2020, 'Lattices for Landau-Ginzburg orbifolds', Mathematische Zeitschrift, vol. 296, no. 1-2, pp. 639-659. https://doi.org/10.1007/s00209-019-02441-3
Ebeling W, Takahashi A. Lattices for Landau-Ginzburg orbifolds. Mathematische Zeitschrift. 2020 Oct;296(1-2):639-659. Epub 2019 Dec 5. doi: 10.1007/s00209-019-02441-3
Ebeling, Wolfgang ; Takahashi, Atsushi. / Lattices for Landau-Ginzburg orbifolds. In: Mathematische Zeitschrift. 2020 ; Vol. 296, No. 1-2. pp. 639-659.
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