Higher dimensional tautological inequalities and applications

Carlo Gasbarri (1) , Gianluca Pacienza (1) , Erwan Rousseau (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several degeneracy statements.

Mots clés: foliations; holomorphic maps; varieties of general type; Green-Griffiths conjecture; tautological inequalities

Domaines: Géométrie algébrique [math.AG]

Carlo Gasbarri, Gianluca Pacienza, Erwan Rousseau. Higher dimensional tautological inequalities and applications. 2010. ⟨hal-00495363v1⟩