Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by S. Cantat.

Thomas Delzant (1) , Pierre Py (1) , Serge Cantat (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 IRMAR - Institut de Recherche Mathématique de Rennes

Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least three factors through a homomorphism onto a cocompact discrete subgroup of PSL 2 (R). We also study actions of Kähler 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.

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Thomas Delzant, Pierre Py, Serge Cantat. Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by S. Cantat.. Compositio Mathematica, 2012, ⟨10.1112/S0010437X11007068⟩. ⟨hal-01262108⟩