Sébastien Boucksom ; Simone Diverio - A note on Lang's conjecture for quotients of bounded domains

epiga:6050 - Épijournal de Géométrie Algébrique, 25 mars 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.volume5.6050
A note on Lang's conjecture for quotients of bounded domainsArticle

Auteurs : Sébastien Boucksom ; Simone Diverio

    It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this conjecture for projective manifolds whose universal cover carries a bounded, strictly plurisubharmonic function. This includes in particular compact free quotients of bounded domains.

    Comment: 10 pages, no figures, comments are welcome. v3: following suggestions made by the referee, the exposition has been improved all along the paper, we added a variant of Theorem A which includes manifolds whose universal cover admits a bounded psh function which is strictly psh just at one point, and we added a section of examples. Final version, to appear on \'Epijournal Géom.
    Algébrique


    Volume : Volume 5
    Publié le : 25 mars 2021
    Accepté le : 25 mars 2021
    Soumis le : 24 janvier 2020
    Mots-clés : Mathematics - Complex Variables, Mathematics - Algebraic Geometry, 32Q15 (Primary), 32Q05 (Secondary)
    Financement :
      Source : OpenAIRE Graph
    • Foliations and algebraic geometry; Financeur: French National Research Agency (ANR); Code: ANR-16-CE40-0008

    Datasets

    Est lié à
    Brunebarbe, Y. (2016). A strong hyperbolicity property of locally symmetric varieties. CIRM. 10.24350/CIRM.V.18991003 1
    • 1 ScholeXplorer

    2 Documents citant cet article

    Statistiques de consultation

    Cette page a été consultée 770 fois.
    Le PDF de cet article a été téléchargé 752 fois.