Holomorphic actions, Kummer examples, and Zimmer Program

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 compact Kähler manifolds $M$ of dimension $n\geq 3$ on which acts a lattice of an almost simple real Lie group of rank $\geq n-1$. This provides a new line in the so-called Zimmer program, and characterizes certain type of complex tori by a property of their automorphisms groups.

Mots clés: automorphism group; Torus; Frame; Lie group; action compact manifold

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

Serge Cantat, Abdelghani Zeghib. Holomorphic actions, Kummer examples, and Zimmer Program. Annales Scientifiques de l'École Normale Supérieure, 2012, 45 (3), pp.447-489. ⟨hal-00538251⟩