Français
Improved bounds for jet differential operators and the Kobayashi conjecture
Post-edited
Authors : Demailly, Jean-Pierre (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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
MSC Codes : 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)
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 27/02/2019 Conference Date : 18/02/2019 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:08:14 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-02-18_Demailly.mp4 
|
Information on the Event
Event Title : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletagesEvent Organizers : Brotbek, Damian ; Diverio, Simone ; Gasbarri, Carlo ; Rousseau, Erwan Dates : 18/02/2019 - 22/02/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2102.html
Citation Data
DOI : 10.24350/CIRM.V.19494503Cite 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 |
See Also
- [Multi angle] Isotriviality for families given by regular foliations / Author of the conference Amerik, Ekaterina.
- [Multi angle] Special manifolds, the core fibration, rational and entire curves / Author of the conference Campana, Frédéric.
- [Multi angle] Arithmetic and algebraic hyperbolicity / Author of the conference Javanpeykar, Ariyan.
- [Multi angle] A Grassmannian technique and the Kobayashi Conjecture / Author of the conference Riedl, Eric.
Bibliography
- Brotbek, D. (2017). On the hyperbolicity of general hypersurfaces. Publications mathématiques de l'IHÉS, 126, 1-34 - https://doi.org/10.1007/s10240-017-0090-3
- Demailly, J.-P. (2018). Recent results on the Kobayashi and Green-Griffiths-Lang conjectures.
- Demailly, J.-P. (1997). Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials. In J. Kollár, & R. Lazarsfeld (Eds.), Algebraic geometry. Proceedings of the Summer Research Institute, Santa Cruz, CA, USA, July 9-29, 1995 (pp. 285-360). Providence, RI: American Mathematical Society - https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/hyperbolic.pdf
- Deng, Y. (2018). On the Diverio-Trapani conjecture.
- Diverio, S., Merker, J., & Rousseau, E. (2010). Effective algebraic degeneracy. Inventiones Mathematicae, 180(1), 161-223 - https://doi.org/10.1007/s00222-010-0232-4
- Nadel, A. (1989). Hyperbolic surfaces in $\mathbb{P}^3$. Duke Mathematical Journal, 58(3), 749-771 - https://doi.org/10.1215/S0012-7094-89-05835-3
- Shiffman, B., & Zaidenberg, M. (2002). Hyperbolic hypersurfaces in $\mathbb{P}^n$ of Fermat-Waring type. Proceedings of the American Mathematical Society, 130(7), 2031-2035 - https://doi.org/10.1090/S0002-9939-01-06417-6
- Siu, Y.-T., & Yeung, S.-K.: Hyperbolicity of the complement of a generic smooth curve of high degree in the complex projective plane. Inventiones Mathematicae, 124(1-3), 573-618 - https://doi.org/10.1007/s002220050064
