Geodesic
On the hyperbolicity of general hypersurfaces
Brotbek, Damian1 idref
1Institut de Recherche Mathématique Avancée, Université de Strasbourg Strasbourg France
Publications Mathématiques de l'IHÉS, Tome 126 (2017), pp. 1-34

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In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in Pn 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.

DOI : 10.1007/s10240-017-0090-3

Brotbek, Damian  1

1 Institut de Recherche Mathématique Avancée, Université de Strasbourg Strasbourg France 
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
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     title = {On the hyperbolicity of general hypersurfaces},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--34},
     year = {2017},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {126},
     doi = {10.1007/s10240-017-0090-3},
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