Holomorphic actions, Kummer examples, and Zimmer program
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, pp. 447-489.

We classify compact Kähler manifolds M of dimension n3 on which acts a lattice of an almost simple real Lie group of rank n-1. This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.

Nous classons les variétés compactes kählériennes M de dimension n3 munies d’une action d’un réseau Γ dans un groupe de Lie réel presque simple de rang n-1. Ceci complète le programme de Zimmer dans ce cadre, et caractérise certains tores complexes compacts par des propriétés de leur groupe d’automorphismes.

DOI: 10.24033/asens.2170
Classification: 22E40,  32J27
Keywords: lattices, superrigidity, complex tori, automorphism groups, Hodge theory, invariant cones, holomorphic dynamics
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Cantat, Serge; Zeghib, Abdelghani. Holomorphic actions, Kummer examples, and Zimmer program. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, pp. 447-489. doi : 10.24033/asens.2170. http://www.numdam.org/articles/10.24033/asens.2170/

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