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dc.contributor.authorJavanpeykar, Ariyan
dc.contributor.authorKamenova, Ljudmila
dc.date.accessioned2018-10-08T12:46:44Z
dc.date.available2018-10-08T12:46:44Z
dc.date.issued2018-10-08
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1387
dc.description.abstractDemailly'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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,20
dc.subjectHyperbolicityen_US
dc.subjectModuli of mapsen_US
dc.subjectBoundednessen_US
dc.subjectHom-schemesen_US
dc.titleDemailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Mapsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-20
local.scientificprogramOWLF 2018en_US
local.series.idOWP-2018-20en_US
local.subject.msc32en_US
local.subject.msc37en_US
local.subject.msc14en_US


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