Weil Classes and Decomposable Abelian Fourfolds
We determine which codimension two Hodge classes on 𝐽 × 𝐽, where 𝐽 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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211807 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Weil Classes and Decomposable Abelian Fourfolds. Bert van Geemen. SIGMA 18 (2022), 097, 18 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We determine which codimension two Hodge classes on 𝐽 × 𝐽, where 𝐽 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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| ISSN: | 1815-0659 |