Positivity, plethysm and hyperbolicity of Siegel varieties in positive characteristic
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917003548164096 |
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| author | Alexandre, Thibault |
| author_facet | Alexandre, Thibault |
| contents | We study hyperbolicity properties of the moduli space of polarized abelian varieties (also known as the Siegel modular variety) in characteristic $p$. Our method uses the plethysm operation for Schur functors as a key ingredient and requires a new positivity notion for vector bundles in characteristic $p$ called $(φ,D)$-ampleness. Generalizing what was known for the Hodge line bundle, we also show that many automorphic vector bundles on the Siegel modular variety are $(φ,D)$-ample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_05804 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Positivity, plethysm and hyperbolicity of Siegel varieties in positive characteristic Alexandre, Thibault Algebraic Geometry 14G35 (Primary) 14G17, 14C99 (Secondary) We study hyperbolicity properties of the moduli space of polarized abelian varieties (also known as the Siegel modular variety) in characteristic $p$. Our method uses the plethysm operation for Schur functors as a key ingredient and requires a new positivity notion for vector bundles in characteristic $p$ called $(φ,D)$-ampleness. Generalizing what was known for the Hodge line bundle, we also show that many automorphic vector bundles on the Siegel modular variety are $(φ,D)$-ample. |
| title | Positivity, plethysm and hyperbolicity of Siegel varieties in positive characteristic |
| topic | Algebraic Geometry 14G35 (Primary) 14G17, 14C99 (Secondary) |
| url | https://arxiv.org/abs/2206.05804 |