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arXiv · 2310.06784

Finiteness of pointed maps to moduli spaces of polarized varieties

Ariyan Javanpeykar·Steven Lu·Ruiran Sun·Kang Zuo
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Abstract

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.

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Ariyan Javanpeykar, Steven Lu, Ruiran Sun, Kang Zuo. 2023-10-10. Finiteness of pointed maps to moduli spaces of polarized varieties. https://arxiv.org/abs/2310.06784

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