Periods of Real Biextensions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916670388305920 |
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| author | Hain, Richard |
| author_facet | Hain, Richard |
| contents | A real biextension is a real mixed Hodge structure that is an extension of R(0) by a mixed Hodge structure with weights $-1$ and $-2$. A unipotent real biextension over an algebraic manifold is a variation of mixed Hodge structure over it, each of whose fibers is a real biextension and whose weight graded quotients are do not vary. We show that if a unipotent real biextension has non abelian monodromy, then its ``general fiber'' does not split. This result is a tool for investigating the boundary behaviour of normal functions and is applied in arXiv:2408.07809 to study the boundary behaviour of the normal function of the Ceresa cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periods of Real Biextensions Hain, Richard Algebraic Geometry 14C30 A real biextension is a real mixed Hodge structure that is an extension of R(0) by a mixed Hodge structure with weights $-1$ and $-2$. A unipotent real biextension over an algebraic manifold is a variation of mixed Hodge structure over it, each of whose fibers is a real biextension and whose weight graded quotients are do not vary. We show that if a unipotent real biextension has non abelian monodromy, then its ``general fiber'' does not split. This result is a tool for investigating the boundary behaviour of normal functions and is applied in arXiv:2408.07809 to study the boundary behaviour of the normal function of the Ceresa cycle. |
| title | Periods of Real Biextensions |
| topic | Algebraic Geometry 14C30 |
| url | https://arxiv.org/abs/2408.13997 |