K\"ahler groups, real hyperbolic spaces and the Cremona group
Algebraic Geometry
2019-02-20 v2 Differential Geometry
Group Theory
Abstract
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.
Cite
@article{arxiv.1012.1585,
title = {K\"ahler groups, real hyperbolic spaces and the Cremona group},
author = {Thomas Delzant and Pierre Py},
journal= {arXiv preprint arXiv:1012.1585},
year = {2019}
}
Comments
Referee's comments and minor corrections included. With an appendix by Serge Cantat