Geodesic
Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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: orbifold Euler characteristic, mirror symmetry, Berglund–Hübsch–Henningson–Takahashi duality.
Mots-clés : group action, invertible polynomial 
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Wolfgang Ebeling; Sabir M. Gusein-Zade. Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a50/

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