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This article is cited in 4 scientific papers (total in 4 papers)
Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic
Wolfgang Ebelinga, Sabir M. Gusein-Zadeb a Leibniz Universität Hannover, Institut für Algebraische Geometrie, Postfach 6009, D-30060 Hannover, Germany
b Moscow State University, Faculty of Mechanics and Mathematics,
Moscow, GSP-1, 119991, Russia
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:
group action, invertible polynomial, orbifold Euler characteristic, mirror symmetry, Berglund–Hübsch–Henningson–Takahashi duality.
Received: July 29, 2019; in final form June 1, 2020; Published online June 11, 2020
Citation:
Wolfgang Ebeling, Sabir M. Gusein-Zade, “Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic”, SIGMA, 16 (2020), 051, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1588 https://www.mathnet.ru/eng/sigma/v16/p51
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