Authors:	Javanpeykar, Ariyan Kucharczyk, Robert
Title:	Algebraicity of analytic maps to a hyperbolic variety
Online publication date:	6-Aug-2021
Year of first publication:	2020
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
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-6245
Version:	Published version
Publication type:	Zeitschriftenaufsatz
Document type specification:	Scientific article
License:	CC BY-NC
Information on rights of use:	https://creativecommons.org/licenses/by-nc/4.0/
Journal:	Mathematische Nachrichten 293 8
Pages or article number:	1490 1504
Publisher:	Wiley-VCH
Publisher place:	Weinheim
Issue date:	2020
ISSN:	1522-2616
Publisher URL:	https://doi.org/10.1002/mana.201900098
Publisher DOI:	10.1002/mana.201900098
Appears in collections:	JGU-Publikationen