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Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic

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

Autorschaft

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Organisationseinheiten

Externe Organisationen

  • Lomonosov Moscow State University

Details

OriginalspracheEnglisch
Aufsatznummer051
Seiten (von - bis)1-15
Seitenumfang15
FachzeitschriftSIGMA
Jahrgang16
Ausgabenummer51
PublikationsstatusVeröffentlicht - 11 Juni 2020

Abstract

P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi–Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construction to symmetry groups generated by some diagonal symmetries and some permutations of variables. In a previous paper, we explained that this construction should work only under a special condition on the permutation group called parity condition (PC). Here we prove that, if the permutation group is cyclic and satisfies PC, then the reduced orbifold Euler characteristics of the Milnor fibres of dual pairs coincide up to sign.

ASJC Scopus Sachgebiete

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Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
in: SIGMA, Jahrgang 16, Nr. 51, 051, 11.06.2020, S. 1-15.

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

Ebeling W, Gusein-Zade SM. Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. SIGMA. 2020 Jun 11;16(51):1-15. 051. doi: 10.3842/SIGMA.2020.051
Ebeling, Wolfgang ; Gusein-Zade, Sabir M. / Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. in: SIGMA. 2020 ; Jahrgang 16, Nr. 51. S. 1-15.
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AU - Gusein-Zade, Sabir M.

N1 - Funding information: This work was partially supported by DFG. The work of the second author (Sections 2 and 4) was supported by the grant 16-11-10018 of the Russian Foundation for Basic Research. We are very grateful to the referees of the paper for their useful comments.

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