# Normal subgroups in the Cremona group

@article{Cantat2010NormalSI,
title={Normal subgroups in the Cremona group},
author={Serge Cantat and St'ephane Lamy and Yves Cornulier},
journal={Acta Mathematica},
year={2010},
volume={210},
pages={31-94}
}
• Published 2010
• Mathematics
• Acta Mathematica
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.
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