Equations differentielles sur les hypersurfaces de l'espace projectif complexe de dimension 4

Erwan Rousseau (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The main goal of this work is to prove that every entire curve in a smooth hypersurface of degree greater than or equal to 97 in the complex projective space of dimension 4 must satisfy an algebraic differential equation of order 3. A logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree greater than or equal to 92 in the complex projective space of dimension 3 must satisfy an algebraic differential equation of order 3.

Mots clés: hyperbolicité au sens de Kobayashi; courbes entières

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

Erwan Rousseau. Equations differentielles sur les hypersurfaces de l'espace projectif complexe de dimension 4. Journal de Mathématiques Pures et Appliquées, 2006, 86, pp.322-341. ⟨10.1016/j.matpur.2006.06.004⟩. ⟨hal-00135325⟩