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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210699 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862623137681637376 |
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| author | Ebeling, Wolfgang Gusein-Zade, Sabir M. |
| author_facet | Ebeling, Wolfgang Gusein-Zade, Sabir M. |
| citation_txt | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. Wolfgang Ebeling and Sabir M. Gusein-Zade. SIGMA 16 (2020), 051, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-17T12:04:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210699 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:31Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ebeling, Wolfgang Gusein-Zade, Sabir M. 2025-12-15T15:24:07Z 2020 Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic. Wolfgang Ebeling and Sabir M. Gusein-Zade. SIGMA 16 (2020), 051, 15 pages 1815-0659 2020 Mathematics Subject Classification: 14J33; 57R18; 32S55 arXiv:1907.11421 https://nasplib.isofts.kiev.ua/handle/123456789/210699 https://doi.org/10.3842/SIGMA.2020.051 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic Article published earlier |
| spellingShingle | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic Ebeling, Wolfgang Gusein-Zade, Sabir M. |
| title | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic |
| title_full | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic |
| title_fullStr | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic |
| title_full_unstemmed | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic |
| title_short | Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic |
| title_sort | dual invertible polynomials with permutation symmetries and the orbifold euler characteristic |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210699 |
| work_keys_str_mv | AT ebelingwolfgang dualinvertiblepolynomialswithpermutationsymmetriesandtheorbifoldeulercharacteristic AT guseinzadesabirm dualinvertiblepolynomialswithpermutationsymmetriesandtheorbifoldeulercharacteristic |