Algebraicity of analytic maps to a hyperbolic variety

2018/06/25 by Javanpeykar, Ariyan, Kucharczyk, Robert A. · 2 citations
#32Q45 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.09338

Abstract

Let X be an algebraic variety over ℂ. We say that X is Borel hyperbolic if, for every finite type reduced scheme S over ℂ, every holomorphic map S^an→ X^an is algebraic. We use a transcendental specialization technique to prove that X is Borel hyperbolic if and only if, for every smooth affine curve C over ℂ, every holomorphic map C^an→ X^an is algebraic. We use the latter result to prove that Borel hyperbolicity shares many common features with other notions of hyperbolicity such as Kobayashi hyperbolicity.

Cited by

• Real geometric transcendence for uniformization maps of algebraic Riemann surfaces
• Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity

Related

• Non-archimedean hyperbolicity of the moduli space of curves
• Hyperbolic algebraic and analytic curves
• Algebraic intermediate hyperbolicities
• Hyperbolicity of varieties with big linear representation of π₁
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