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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01248 |
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| _version_ | 1866910628391682048 |
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| author | Bakker, Ben Pila, Jonathan Tsimerman, Jacob |
| author_facet | Bakker, Ben Pila, Jonathan Tsimerman, Jacob |
| contents | Given a smooth proper family $ϕ:X\rightarrow S$, we study the (quasi)-periods of the fibers of $ϕ$ as (germs of) functions on $S$. We show that they field they generate has the same algebraic closure as that given by the flag variety co-ordinates parametrizing the corresponding Hodge filtration, together with their derivatives. Moreover, in the more general context of an arbitrary flat vector bundle, we determine the transcendence degree of the function field generated by the flat coordinates of algebraic sections. Our results are inspired by and generalize work of Bertrand--Zudilin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periods in Families and Derivatives of Period Maps Bakker, Ben Pila, Jonathan Tsimerman, Jacob Algebraic Geometry Logic Given a smooth proper family $ϕ:X\rightarrow S$, we study the (quasi)-periods of the fibers of $ϕ$ as (germs of) functions on $S$. We show that they field they generate has the same algebraic closure as that given by the flag variety co-ordinates parametrizing the corresponding Hodge filtration, together with their derivatives. Moreover, in the more general context of an arbitrary flat vector bundle, we determine the transcendence degree of the function field generated by the flat coordinates of algebraic sections. Our results are inspired by and generalize work of Bertrand--Zudilin. |
| title | Periods in Families and Derivatives of Period Maps |
| topic | Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2410.01248 |