Finiteness of pointed maps to moduli spaces of polarized varieties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916798102765568 |
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| author | Javanpeykar, Ariyan Lu, Steven Sun, Ruiran Zuo, Kang |
| author_facet | Javanpeykar, Ariyan Lu, Steven Sun, Ruiran Zuo, Kang |
| contents | We establish a finiteness result for pointed maps to the base space $U$ of a smooth projective family of varieties with maximal variation in moduli. For its proof, we establish the rigidity of pointed maps to a (not necessarily compact) variety which is hyperbolic modulo a proper closed subset. Together with Viehweg's hyperbolicity conjecture on the bigness of log-canonical bundles of moduli spaces, resolved by Campana-Paun, we derive an optimal dimension bound on the Hom scheme from a curve to $U$ among other applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06784 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finiteness of pointed maps to moduli spaces of polarized varieties Javanpeykar, Ariyan Lu, Steven Sun, Ruiran Zuo, Kang Algebraic Geometry Complex Variables We establish a finiteness result for pointed maps to the base space $U$ of a smooth projective family of varieties with maximal variation in moduli. For its proof, we establish the rigidity of pointed maps to a (not necessarily compact) variety which is hyperbolic modulo a proper closed subset. Together with Viehweg's hyperbolicity conjecture on the bigness of log-canonical bundles of moduli spaces, resolved by Campana-Paun, we derive an optimal dimension bound on the Hom scheme from a curve to $U$ among other applications. |
| title | Finiteness of pointed maps to moduli spaces of polarized varieties |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2310.06784 |