Abelian varieties with no power isogenous to a Jacobian
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912686985445376 |
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| author | Fortman, Olivier de Gaay Schreieder, Stefan |
| author_facet | Fortman, Olivier de Gaay Schreieder, Stefan |
| contents | For a curve of genus at least four which is either very general or very general hyperelliptic, we classify all ways in which a power of its Jacobian can be isogenous to a product of Jacobians of curves. As an application, we show that, for a very general principally polarized abelian variety of dimension at least four, or the intermediate Jacobian of a very general cubic threefold, no power is isogenous to a product of Jacobians of curves. This confirms some cases of the Coleman-Oort conjecture. We further deduce from our results some progress on the question whether the integral Hodge conjecture fails for such abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abelian varieties with no power isogenous to a Jacobian Fortman, Olivier de Gaay Schreieder, Stefan Algebraic Geometry Complex Variables Number Theory For a curve of genus at least four which is either very general or very general hyperelliptic, we classify all ways in which a power of its Jacobian can be isogenous to a product of Jacobians of curves. As an application, we show that, for a very general principally polarized abelian variety of dimension at least four, or the intermediate Jacobian of a very general cubic threefold, no power is isogenous to a product of Jacobians of curves. This confirms some cases of the Coleman-Oort conjecture. We further deduce from our results some progress on the question whether the integral Hodge conjecture fails for such abelian varieties. |
| title | Abelian varieties with no power isogenous to a Jacobian |
| topic | Algebraic Geometry Complex Variables Number Theory |
| url | https://arxiv.org/abs/2401.06577 |