On the hyperbolicity of general hypersurfaces

Brotbek, Damian

doi:10.1007/s10240-017-0090-3

Geodesic

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On the hyperbolicity of general hypersurfaces

Brotbek, Damian ¹

¹ Institut de Recherche Mathématique Avancée, Université de Strasbourg Strasbourg France

Publications Mathématiques de l'IHÉS, Tome 126 (2017), pp. 1-34.

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Résumé

In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in $P^{n}$ are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove this statement, we construct hypersurfaces satisfying a property which is Zariski open and which implies hyperbolicity. These hypersurfaces are chosen such that the geometry of their higher order jet spaces can be related to the geometry of a universal family of complete intersections. To do so, we introduce a Wronskian construction which associates a (twisted) jet differential to every finite family of global sections of a line bundle.

MR Zbl

DOI : 10.1007/s10240-017-0090-3

Affiliations des auteurs :

Brotbek, Damian ¹

¹ Institut de Recherche Mathématique Avancée, Université de Strasbourg Strasbourg France

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Brotbek, Damian. On the hyperbolicity of general hypersurfaces. Publications Mathématiques de l'IHÉS, Tome 126 (2017), pp. 1-34. doi : 10.1007/s10240-017-0090-3. http://geodesic.mathdoc.fr/articles/10.1007/s10240-017-0090-3/

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