Non-deformability of entire curves in projective hypersurfaces of high degree
[Non-deformabilité des courbes entières dans les hypersurfaces projectives de grand degré]
Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 247-253.

Dans cet article, nous démontrons qu’il n’existe pas de famille de rang maximal de courbes entières dans la famille universelle des hypersurfaces de degré d2n dans l’espace projectif complexe n . Cela peut se voir comme une version faible de la conjecture de Kobayashi affirmant qu’une hypersurface projective générale de haut degré est hyperbolique au sens de Kobayashi.

In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree d2n in the complex projective space n . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.

DOI : 10.5802/aif.2178
Classification : 14J70, 32Q45
Keywords: projective hypersurfaces, entire curves, Kobayashi hyperbolicity
Mot clés : hypersurfaces projectives, courbes entières, hyperbolicité au sens de Kobayashi
Debarre, Olivier 1 ; Pacienza, Gianluca 2 ; Păun, Mihai 3

1 Université L. Pasteur et CNRS Institut de Recherche Mathématique Avancée 7, rue René Descartes 67084 Strasbourg Cedex (France)
2 Institut de Recherche Mathématique Avancée Université L. Pasteur et CNRS 7, rue René Descartes 67084 Strasbourg Cédex (France)
3 Université Henri Poincaré Nancy 1 Institut Élie Cartan B.P. 239 54506 Vandœuvre-lès-Nancy Cedex (France)
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Debarre, Olivier; Pacienza, Gianluca; Păun, Mihai. Non-deformability of entire curves in projective hypersurfaces of high degree. Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 247-253. doi : 10.5802/aif.2178. http://www.numdam.org/articles/10.5802/aif.2178/

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