Abstract
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.
Note
With an appendix by Yves de Cornulier.
Citation
Serge Cantat. Stéphane Lamy. Yves Cornulier. "Normal subgroups in the Cremona group." Acta Math. 210 (1) 31 - 94, 2013. https://doi.org/10.1007/s11511-013-0090-1
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