Holomorphic actions, Kummer examples, and Zimmer program

Cantat, Serge; Zeghib, Abdelghani

doi:10.24033/asens.2170

Holomorphic actions, Kummer examples, and Zimmer program
[Actions holomorphes, exemples de Kummer et programme de Zimmer]

Cantat, Serge ; Zeghib, Abdelghani

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 45 (2012) no. 3, pp. 447-489.

Résumé
Abstract

Nous classons les variétés compactes kählériennes $M$ de dimension $n \geq 3$ munies d’une action d’un réseau $Γ$ dans un groupe de Lie réel presque simple de rang $\geq n - 1$ . Ceci complète le programme de Zimmer dans ce cadre, et caractérise certains tores complexes compacts par des propriétés de leur groupe d’automorphismes.

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 complex tori as compact Kähler manifolds with large automorphisms groups.

MR Zbl | 1 citation dans Numdam

DOI : 10.24033/asens.2170

Classification : 22E40, 32J27
Keywords: lattices, superrigidity, complex tori, automorphism groups, Hodge theory, invariant cones, holomorphic dynamics
Mot clés : réseaux, super-rigidité, tores complexes, groupes d'automorphismes, théorie de Hodge, cônes invariants, dynamique holomorphe

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     author = {Cantat, Serge and Zeghib, Abdelghani},
     title = {Holomorphic actions, {Kummer} examples, and {Zimmer} program},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {447--489},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 45},
     number = {3},
     year = {2012},
     doi = {10.24033/asens.2170},
     mrnumber = {3014483},
     zbl = {1280.22015},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.2170/}
}

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Cantat, Serge; Zeghib, Abdelghani. Holomorphic actions, Kummer examples, and Zimmer program. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 45 (2012) no. 3, pp. 447-489. doi : 10.24033/asens.2170. https://www.numdam.org/articles/10.24033/asens.2170/

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