Lattices for Landau-Ginzburg orbifolds

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Wolfgang Ebeling
  • Atsushi Takahashi

Organisationseinheiten

Externe Organisationen

  • Osaka University
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)639-659
Seitenumfang21
FachzeitschriftMathematische Zeitschrift
Jahrgang296
Ausgabenummer1-2
Frühes Online-Datum5 Dez. 2019
PublikationsstatusVeröffentlicht - Okt. 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.

Zitieren

Lattices for Landau-Ginzburg orbifolds. / Ebeling, Wolfgang; Takahashi, Atsushi.
in: Mathematische Zeitschrift, Jahrgang 296, Nr. 1-2, 10.2020, S. 639-659.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ebeling, W & Takahashi, A 2020, 'Lattices for Landau-Ginzburg orbifolds', Mathematische Zeitschrift, Jg. 296, Nr. 1-2, S. 639-659. https://doi.org/10.1007/s00209-019-02441-3
Ebeling W, Takahashi A. Lattices for Landau-Ginzburg orbifolds. Mathematische Zeitschrift. 2020 Okt;296(1-2):639-659. Epub 2019 Dez 5. doi: 10.1007/s00209-019-02441-3
Ebeling, Wolfgang ; Takahashi, Atsushi. / Lattices for Landau-Ginzburg orbifolds. in: Mathematische Zeitschrift. 2020 ; Jahrgang 296, Nr. 1-2. S. 639-659.
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