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Algebraicity of analytic maps to a hyperbolic variety

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  • Ariyan Javanpeykar
  • Robert Kucharczyk

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.

Suggested Citation

  • Ariyan Javanpeykar & Robert Kucharczyk, 2020. "Algebraicity of analytic maps to a hyperbolic variety," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1490-1504, August.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:8:p:1490-1504
    DOI: 10.1002/mana.201900098
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