Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic

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

Authors

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Research Organisations

External Research Organisations

  • Lomonosov Moscow State University
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Details

Original languageEnglish
Article number051
Pages (from-to)1-15
Number of pages15
JournalSIGMA
Volume16
Issue number51
Publication statusPublished - 11 Jun 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.

Keywords

    Berglund–Hübsch–Henningson–Takahashi duality, Group action, Invertible polynomial, Mirror symmetry, Orbifold Euler characteristic

ASJC Scopus subject areas

Cite this

Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
In: SIGMA, Vol. 16, No. 51, 051, 11.06.2020, p. 1-15.

Research output: Contribution to journal › Article › Research › 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 ; Vol. 16, No. 51. pp. 1-15.
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