Holomorphic actions, Kummer examples, and Zimmer program
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, p. 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 : https://doi.org/10.24033/asens.2170
Classification:  22E40,  32J27
Keywords: lattices, superrigidity, complex tori, automorphism groups, Hodge theory, invariant cones, holomorphic dynamics
@article{ASENS_2012_4_45_3_447_0,
     author = {Cantat, Serge and Zeghib, Abdelghani},
     title = {Holomorphic actions, Kummer examples, and Zimmer program},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 45},
     number = {3},
     year = {2012},
     pages = {447-489},
     doi = {10.24033/asens.2170},
     zbl = {1280.22015},
     mrnumber = {3014483},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_3_447_0}
}
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/item/ASENS_2012_4_45_3_447_0/

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