dc.contributor.author Javanpeykar, Ariyan dc.contributor.author Kamenova, Ljudmila dc.date.accessioned 2018-10-08T12:46:44Z dc.date.available 2018-10-08T12:46:44Z dc.date.issued 2018-10-08 dc.identifier.uri http://publications.mfo.de/handle/mfo/1387 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_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,20 dc.subject Hyperbolicity en_US dc.subject Moduli of maps en_US dc.subject Boundedness en_US dc.subject Hom-schemes en_US dc.title Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-20 local.scientificprogram OWLF 2018 en_US local.series.id OWP-2018-20 en_US local.subject.msc 32 en_US local.subject.msc 37 en_US local.subject.msc 14 en_US
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