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H 1 A Grassmannian technique and the Kobayashi Conjecture

Auteurs : Riedl, Eric (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces $X$ in $\mathbb{P}^n$: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of $X$, and the Kobayashi Conjecture, which says that X contains no entire curves.
    We prove that (a slightly strengthened version of) the Green-Griffiths-Lang Conjecture in dimension $2n$ implies the Kobayashi Conjecture in dimension $n$. The technique has already led to improved bounds for the Kobayashi Conjecture. This is joint work with David Yang.

    Keywords : Grassmannian technique; Kobayashi Conjecture; jet bundle; variety of general type; Green-Griffiths-Lang Conjecture

    Codes MSC :
    14J70 - Algebraic hypersurfaces
    14M07 - Low-codimension problems
    14M10 - Complete intersections
    32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 27/02/2019
      Date de captation : 18/02/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:58:22
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-02-18_Riedl.mp4

    Informations sur la rencontre

    Nom de la rencontre : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages
    Organisateurs de la rencontre : Brotbek, Damian ; Diverio, Simone ; Gasbarri, Carlo ; Rousseau, Erwan
    Dates : 18/02/2019 - 22/02/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2102.html

    Citation Data

    DOI : 10.24350/CIRM.V.19494903
    Cite this video as: Riedl, Eric (2019). A Grassmannian technique and the Kobayashi Conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19494903
    URI : http://dx.doi.org/10.24350/CIRM.V.19494903

    Voir aussi


    1. Riedl, E., & Yang, D. (2018). Applications of a grassmannian technique in hypersurfaces. - https://arxiv.org/abs/1806.02364