Invariant hypersurfaces in holomorphic dynamics

Serge Cantat (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove the following result, which is analogous to two theorems, one due to Kodaira and Krasnov and another one due to Jouanolou and Ghys. Let M be a compact complex manifold and f a dominant endomorphism of M. If there exist k totally invariant irreducible hypersurfacesWi M, with k > dim(M)+h1,1(M) then f preserves a nontrivial meromorphic fibration. We then study the case where f is a meromorphic map.

Domaines: Systèmes dynamiques [math.DS]

Serge Cantat. Invariant hypersurfaces in holomorphic dynamics. Mathematical Research Letters, 2010, 17 (5), pp.833--841. ⟨hal-00559935⟩