Normal subgroups in the Cremona group (long version)
Algebraic Geometry
2018-04-24 v2 Group Theory
Abstract
Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.
Cite
@article{arxiv.1007.0895,
title = {Normal subgroups in the Cremona group (long version)},
author = {Serge Cantat and Stéphane Lamy},
journal= {arXiv preprint arXiv:1007.0895},
year = {2018}
}
Comments
With an appendix by Yves de Cornulier. Numerous but minors corrections were made, regarding proofs, references and terminology. This long version contains detailled proofs of several technical lemmas about hyperbolic spaces