Finiteness of pointed maps to moduli spaces of polarized varieties

Fuente: arXiv
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Main Authors: Javanpeykar, Ariyan, Lu, Steven, Sun, Ruiran, Zuo, Kang
Format: Preprint
Published: 2023
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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