Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic
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 gener...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210699 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. Wolfgang Ebeling and Sabir M. Gusein-Zade. SIGMA 16 (2020), 051, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 the 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.
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| ISSN: | 1815-0659 |