Gutenberg Open Science: Demailly’s notion of algebraic hyperbolicity : geometricity, boundedness, moduli of maps

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-5862

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DC Field	Value	Language
dc.contributor.author	Javanpeykar, Ariyan	-
dc.contributor.author	Kamenova, Ljudmila	-
dc.date.accessioned	2021-05-17T09:30:13Z	-
dc.date.available	2021-05-17T09:30:13Z	-
dc.date.issued	2020	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/5871	-
dc.description.abstract	Demailly’s conjecture, which is a consequence of the Green–Griffiths–Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence for Demailly’s conjecture by verifying several predictions it makes. We first define what an algebraically hyperbolic projective variety is, extending Demailly’s definition to (not necessarily smooth) projective varieties over an arbitrary algebraically closed field of characteristic zero, and we prove that this property is stable under extensions of algebraically closed fields. Furthermore, we show that the set of (not necessarily surjective) morphisms from a projective variety Y to a projective algebraically hyperbolic variety X that map a fixed closed subvariety of Y onto a fixed closed subvariety of X is finite. As an application, we obtain that Aut(X) is finite and that every surjective endomorphism of X is an automorphism. Finally, we explore “weaker” notions of hyperbolicity related to boundedness of moduli spaces of maps, and verify similar predictions made by the Green–Griffiths–Lang conjecture on hyperbolic projective varieties.	en_GB
dc.language.iso	eng	de
dc.rights	CC BY	*
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	Demailly’s notion of algebraic hyperbolicity : geometricity, boundedness, moduli of maps	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-5862	-
jgu.type.dinitype	article	en_GB
jgu.type.version	Published version	de
jgu.type.resource	Text	de
jgu.organisation.department	FB 08 Physik, Mathematik u. Informatik	de
jgu.organisation.number	7940	-
jgu.organisation.name	Johannes Gutenberg-Universität Mainz	-
jgu.rights.accessrights	openAccess	-
jgu.journal.title	Mathematische Zeitschrift	de
jgu.journal.volume	296	de
jgu.pages.start	1645	de
jgu.pages.end	1672	de
jgu.publisher.year	2020	-
jgu.publisher.name	Springer	de
jgu.publisher.place	Berlin u.a.	de
jgu.publisher.uri	https://doi.org/10.1007/s00209-020-02489-6	de
jgu.publisher.issn	1432-1823	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1007/s00209-020-02489-6
jgu.organisation.ror	https://ror.org/023b0x485
Appears in collections:	JGU-Publikationen

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