Weil Classes and Decomposable Abelian Fourfolds
We determine which codimension two Hodge classes on × , where is a general abelian surface, deform to Hodge classes on a family of abelian fourfolds of Weil type. If a Hodge class deforms, there is, in general, a unique such family. We show how to determine the imaginary quadratic field acting on...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2022 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211807 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Weil Classes and Decomposable Abelian Fourfolds. Bert van Geemen. SIGMA 18 (2022), 097, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575884776505344 |
|---|---|
| author | van Geemen, Bert |
| author_facet | van Geemen, Bert |
| citation_txt | Weil Classes and Decomposable Abelian Fourfolds. Bert van Geemen. SIGMA 18 (2022), 097, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We determine which codimension two Hodge classes on × , where is a general abelian surface, deform to Hodge classes on a family of abelian fourfolds of Weil type. If a Hodge class deforms, there is, in general, a unique such family. We show how to determine the imaginary quadratic field acting on the fourfolds of Weil type in this family, as well as their polarization. There are Hodge classes that may deform to more than one family. We relate these to Markman's Cayley classes.
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| first_indexed | 2026-03-13T14:40:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211807 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T14:40:09Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van Geemen, Bert 2026-01-12T10:13:20Z 2022 Weil Classes and Decomposable Abelian Fourfolds. Bert van Geemen. SIGMA 18 (2022), 097, 18 pages 1815-0659 2020 Mathematics Subject Classification: 14C30; 14C25; 14K20 arXiv:2108.02087 https://nasplib.isofts.kiev.ua/handle/123456789/211807 https://doi.org/10.3842/SIGMA.2022.097 We determine which codimension two Hodge classes on × , where is a general abelian surface, deform to Hodge classes on a family of abelian fourfolds of Weil type. If a Hodge class deforms, there is, in general, a unique such family. We show how to determine the imaginary quadratic field acting on the fourfolds of Weil type in this family, as well as their polarization. There are Hodge classes that may deform to more than one family. We relate these to Markman's Cayley classes. Discussions with E. Markman, K.G. O’Grady, F. Russo, and C. Schoen were very helpful. I thank the referees for their comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Weil Classes and Decomposable Abelian Fourfolds Article published earlier |
| spellingShingle | Weil Classes and Decomposable Abelian Fourfolds van Geemen, Bert |
| title | Weil Classes and Decomposable Abelian Fourfolds |
| title_full | Weil Classes and Decomposable Abelian Fourfolds |
| title_fullStr | Weil Classes and Decomposable Abelian Fourfolds |
| title_full_unstemmed | Weil Classes and Decomposable Abelian Fourfolds |
| title_short | Weil Classes and Decomposable Abelian Fourfolds |
| title_sort | weil classes and decomposable abelian fourfolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211807 |
| work_keys_str_mv | AT vangeemenbert weilclassesanddecomposableabelianfourfolds |