Improved bounds for jet differential operators and the Kobayashi conjecture | Vidéo | Carmin.tv

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Chapters

Improved bounds for jet differential operators and the Kobayashi conjecture

By Jean-Pierre Demailly

Appears in collection : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages

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.

Information about the video

Date of recording 18/02/2019
Date of publication 27/02/2019
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19494503
Cite this video Demailly, Jean-Pierre (18/02/2019). Improved bounds for jet differential operators and the Kobayashi conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19494503
URL https://dx.doi.org/10.24350/CIRM.V.19494503

Domain(s)

Algebraic Geometry

Bibliography

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Demailly, J.-P. (2018). Recent results on the Kobayashi and Green-Griffiths-Lang conjectures. <arXiv:1801.04765> - https://arxiv.org/abs/1801.04765
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
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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

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