English
Improved bounds for jet differential operators and the Kobayashi conjecture
Post-edited
Auteurs : Demailly, Jean-Pierre (Auteur de la Conférence)
CIRM (Editeur )
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)
CIRM (Editeur )
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 : 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
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)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 27/02/2019 Date de captation : 18/02/2019 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 01:08:14 Audience : Researchers Download : https://videos.cirm-math.fr/2019-02-18_Demailly.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletagesOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19494503Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Isotriviality for families given by regular foliations / Auteur de la Conférence Amerik, Ekaterina.
- [Multi angle] Special manifolds, the core fibration, rational and entire curves / Auteur de la Conférence Campana, Frédéric.
- [Multi angle] Arithmetic and algebraic hyperbolicity / Auteur de la Conférence Javanpeykar, Ariyan.
- [Multi angle] A Grassmannian technique and the Kobayashi Conjecture / Auteur de la Conférence Riedl, Eric.
Bibliographie
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- Demailly, J.-P. (2018). Recent results on the Kobayashi and Green-Griffiths-Lang conjectures.
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