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Increasing hyperbolicity of varieties supporting a variation of Hodge structures with level structures
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
| dc.contributor.author | BRUNEBARBE, Yohan | |
| dc.date.accessioned | 2024-04-04T02:48:21Z | |
| dc.date.available | 2024-04-04T02:48:21Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191732 | |
| dc.description.abstractEn | Looking at the finite \'etale congruence covers $X(p)$ of a complex algebraic variety $X$ equipped with a variation of integral polarized Hodge structures whose period map is quasi-finite, we show that both the minimal gonality among all curves contained in $X(p)$ and the minimal volume among all subvarieties of $X(p)$ tend to infinity with $p$. This applies for example to Shimura varieties, moduli spaces of curves, moduli spaces of abelian varieties, moduli spaces of Calabi-Yau varieties, and can be made effective in many cases. The proof goes roughly as follows. We first prove a generalization of the Arakelov inequalities valid for any variation of Hodge structures on higher-dimensional algebraic varieties, which implies that the hyperbolicity of the subvarieties of $X$ is controlled by the positivity of a single line bundle. We then show in general that a big line bundle on a normal proper algebraic variety $\bar X$ can be made more and more positive by going to finite covers of $\bar X$ defined using level structures of a local system defined on a Zariski-dense open subset. | |
| dc.language.iso | en | |
| dc.title.en | Increasing hyperbolicity of varieties supporting a variation of Hodge structures with level structures | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2007.12965 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03064502 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03064502v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BRUNEBARBE,%20Yohan&rft.genre=preprint |
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