Algebraicity of analytic maps to a hyperbolic variety

Ariyan Javanpeykar and Robert Kucharczyk

Mathematische Nachrichten, 2020, vol. 293, issue 8, 1490-1504

Abstract: Let X be a complex algebraic variety. We say that X is Borel hyperbolic if, for every finite type reduced scheme S over the complex numbers, every holomorphic map from S to X is algebraic. We use a transcendental specialization technique to prove that X is Borel hyperbolic if and only if, for every smooth affine complex algebraic curve C, every holomorphic map from C to X 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.

Date: 2020
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https://doi.org/10.1002/mana.201900098

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