Holomorphic actions of higher rank lattices in dimension three

Serge Cantat (1) , Abdelghani Zeghib (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We classify all holomorphic actions of higher rank lattices on compact Kaehler manifolds of dimension 3. This provides a complete answer to Zimmer's program for holomorphic actions on compact Kaehler manifolds of dimension at most 3.

Domaines: Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Serge Cantat, Abdelghani Zeghib. Holomorphic actions of higher rank lattices in dimension three. 2009. ⟨hal-00414118⟩