Logarithmic vector fields and hyperbolicity

Erwan Rousseau (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In this article we prove that the complement of a very generic curve of degree at least equal to 14 in the complex projective plane is hyperbolic in the sense of Kobayashi. Thus, using a new method, we improve the former known bound obtained by El Goul. We also improve the case of a very generic curve with two components.

Mots clés: Kobayashi hyperbolicity; jet differentials; logarithmic vector fields

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Erwan Rousseau. Logarithmic vector fields and hyperbolicity. 2007. ⟨hal-00174591v2⟩