# MathSciDoc: An Archive for Mathematician ∫

#### Group Theory and Lie Theorymathscidoc:1701.01003

Acta Mathematica, 210, (1), 31-94, 2010.7
Let$k$be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $$\mathbb{P}_{\mathbf{k}}^2$$ 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.
@inproceedings{serge2010normal,
title={Normal subgroups in the Cremona group},
author={Serge Cantat, Stéphane Lamy, and Yves de Cornulier},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400198804766},
booktitle={Acta Mathematica},
volume={210},
number={1},
pages={31-94},
year={2010},
}

Serge Cantat, Stéphane Lamy, and Yves de Cornulier. Normal subgroups in the Cremona group. 2010. Vol. 210. In Acta Mathematica. pp.31-94. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400198804766.