Higher dimensional tautological inequalities and applications

Carlo Gasbarri (1) , Gianluca Pacienza (1) , Erwan Rousseau (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 I2M - Institut de Mathématiques de Marseille

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

Mots clés: algebraic degeneracy; foliations; canonical singularities; Ahlfors currents; Green-Griffiths-Lang conjecture; tautological inequalities; algebraic degeneracy.

Domaines: Géométrie algébrique [math.AG]

Carlo Gasbarri, Gianluca Pacienza, Erwan Rousseau. Higher dimensional tautological inequalities and applications. Mathematische Annalen, 2013. ⟨hal-00495363v2⟩