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dc.contributor.authorJavanpeykar, Ariyan
dc.contributor.authorKamenova, Ljudmila
dc.date.accessioned2020-01-23T08:09:58Z
dc.date.available2020-01-23T08:09:58Z
dc.date.issued2020-01-23
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3694
dc.description.abstractDemailly's conjecture, which is a consequence of the Green-Griffths-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-Griffths-Lang conjecture on hyperbolic projective varieties.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,20.2
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 Maps (Revised Edition)en_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2018-20.2
local.scientificprogramOWLF 2018en_US
local.series.idOWP-2018-20.2en_US
local.subject.msc32en_US
local.subject.msc37en_US
local.subject.msc14en_US
dc.identifier.urnurn:nbn:de:101:1-2024031913545671865992
dc.identifier.ppn188379689X


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