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H 2 Improved bounds for jet differential operators and the Kobayashi conjecture

Auteurs : Demailly, Jean-Pierre (Auteur de la Conférence)
CIRM (Editeur )

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definition of a hyperbolic variety statement of the Kobayashi conjecture use of jet differential operators fundamental vanishing theorem existence theorem for jet differentials Wronskian operators construction of many divisible Wronskians and main theorem Semple bundles Wronskian ideal sheaf construction of a good algebraic hypersurface possessing many Wronskians questions from the audience

Résumé : We will discuss several new ideas that can show the existence of jet differential operators on arbitrary projective varieties, and also on general hypersurfaces of $\mathbb{P}^n$ of sufficiently high degree. These results can be applied to improve degree bounds in several hyperbolicity problems and especially in the proof of the Kobayashi conjecture.

Keywords : Brody curve; hyperbolic variety; variety of general type; Kobayashi pseudometric; Kobayashi conjecture; Green-Griffiths-Lang conjecture; jet differential; fundamental vanishing theorem; Wronskian operator; Semple bundles; Wronskian ideal sheaf

Codes MSC :
14J40 - Algebraic $n$-folds ($n>4$)
32L10 - Sheaves and cohomology of sections of holomorphic vector bundles, general results
32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds
53C55 - Hermitian and Kählerian manifolds (global differential geometry)

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 27/02/2019
    Date de captation : 18/02/2019
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 01:08:14
    Domaine : Algebraic & Complex Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2019-02-18_Demailly.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.19494503
Cite this video as: Demailly, Jean-Pierre (2019). Improved bounds for jet differential operators and the Kobayashi conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19494503
URI : http://dx.doi.org/10.24350/CIRM.V.19494503

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