Kähler groups, real hyperbolic spaces and the Cremona group

Details Kähler groups, real hyperbolic spaces and the Cremona group Kähler groups, real hyperbolic spaces and the Cremona group

2010-12-07

arxiv.org/abs/1012.1585v2

Compositio Math. 148, no. 1 (2012), 153--184

Mathematics

Algebraic Geometry

Referee's comments and minor corrections included. With an appendix by Serge Cantat

Scientific paper

10.1112/S0010437X11007068

Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a K\"{a}hler group on the real hyperbolic space of dimension at least 3 factors through a homomorphism onto a cocompact discrete subgroup of PSL(2,R). We also study actions of K\"{a}hler groups on infinite dimensional real hyperbolic spaces, describe some exotic actions of PSL(2,R) on these spaces, and give an application to the study of the Cremona group.

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