Non-deformability of entire curves in projective hypersurfaces of high degree

[Non-deformabilité des courbes entières dans les hypersurfaces projectives de grand degré]

Debarre, Olivier ; Pacienza, Gianluca ; Păun, Mihai

Annales de l'Institut Fourier, Tome 56 (2006), p. 247-253 / Harvested from Numdam

Résumé

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 $d\ge 2n$ dans l’espace projectif complexe ${\mathbb{P}}^n$. 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.

Abstract

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 $d\ge 2n$ in the complex projective space ${\mathbb{P}}^n$. 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.

Détail

Publié le : 2006-01-01

MR 2228686 | Zbl 1096.32010

DOI : https://doi.org/10.5802/aif.2178
Classification:  14J70,  32Q45
Mots clés: hypersurfaces projectives,courbes entières,hyperbolicité au sens de Kobayashi

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