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Pré-Publication, Document De Travail Année : 2015

Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces

Jean-Pierre Demailly

Résumé

The Green-Griffiths-Lang conjecture stipulates that for every projective variety $X$ of general type over ${\mathbb C}$, there exists a proper algebraic subvariety of $X$ containing all non constant entire curves $f:{\mathbb C}\to X$. Using the formalism of directed varieties, we prove here that this assertion holds true in case $X$ satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle $T_X$. We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurface of dimension $n$ and degree at least $2n+2$ in the complex projective space ${\mathbb P}^{n+1}$ is hyperbolic.
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Dates et versions

hal-01109166 , version 1 (25-01-2015)
hal-01109166 , version 2 (14-02-2015)
hal-01109166 , version 3 (11-03-2015)

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Citer

Jean-Pierre Demailly. Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces. 2015. ⟨hal-01109166v3⟩

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