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Authors: Javanpeykar, Ariyan
Kucharczyk, Robert
Title: Algebraicity of analytic maps to a hyperbolic variety
Online publication date: 6-Aug-2021
Language: english
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.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
Version: Published version
Publication type: Zeitschriftenaufsatz
Document type specification: Scientific article
License: CC BY-NC
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Journal: Mathematische Nachrichten
Pages or article number: 1490
Publisher: Wiley-VCH
Publisher place: Weinheim
Issue date: 2020
ISSN: 1522-2616
Publisher URL:
Publisher DOI: 10.1002/mana.201900098
Appears in collections:JGU-Publikationen

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