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http://doi.org/10.25358/openscience-5862
Autoren: | Javanpeykar, Ariyan Kamenova, Ljudmila |
Titel: | Demailly’s notion of algebraic hyperbolicity : geometricity, boundedness, moduli of maps |
Online-Publikationsdatum: | 17-Mai-2021 |
Erscheinungsdatum: | 2020 |
Sprache des Dokuments: | Englisch |
Zusammenfassung/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. |
DDC-Sachgruppe: | 510 Mathematik 510 Mathematics |
Veröffentlichende Institution: | Johannes Gutenberg-Universität Mainz |
Organisationseinheit: | FB 08 Physik, Mathematik u. Informatik |
Veröffentlichungsort: | Mainz |
ROR: | https://ror.org/023b0x485 |
DOI: | http://doi.org/10.25358/openscience-5862 |
Version: | Published version |
Publikationstyp: | Zeitschriftenaufsatz |
Nutzungsrechte: | CC BY |
Informationen zu den Nutzungsrechten: | https://creativecommons.org/licenses/by/4.0/ |
Zeitschrift: | Mathematische Zeitschrift 296 |
Seitenzahl oder Artikelnummer: | 1645 1672 |
Verlag: | Springer |
Verlagsort: | Berlin u.a. |
Erscheinungsdatum: | 2020 |
ISSN: | 1432-1823 |
URL der Originalveröffentlichung: | https://doi.org/10.1007/s00209-020-02489-6 |
DOI der Originalveröffentlichung: | 10.1007/s00209-020-02489-6 |
Enthalten in den Sammlungen: | JGU-Publikationen |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | ||
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javanpeykar_ariyan-demailly’s_not-20210430100222299.pdf | 441.4 kB | Adobe PDF | Öffnen/Anzeigen |