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Annales scientifiques de l'ENS - Parutions - série 4, 45 (2012)

Parutions < série 4, 45

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 45, fascicule 3 (2012)

Serge Cantat, Abdelghani Zeghib
Holomorphic actions, Kummer examples, and Zimmer Program
Annales scientifiques de l'ENS 45, fascicule 3 (2012), 447-489

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Résumé :
Actions holomorphes, exemples de Kummer et programme de Zimmer
Nous classons les variétés compactes kählériennes M de dimension n3 munies d'une action d'un réseau 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.

Mots-clefs : Réseaux, super-rigidité, tores complexes, groupes d'automorphismes, théorie de Hodge, cônes invariants, dynamique holomorphe

Abstract:
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.

Keywords: Lattices, superrigidity, complex tori, automorphism groups, Hodge theory, invariant cones, holomorphic dynamics

Class. math. : 22E40; 32J27


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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