Normal subgroups in the Cremona group

Serge Cantat Université de Rennes I, Campus de Beaulieu, Bâtiment 22-23, Rennes Cedex, France Stéphane Lamy Mathematics Institute, University of Warwick Yves de Cornulier Laboratoire de Mathématiques d’Orsay, CNRS & Université Paris-Sud 11

Group Theory and Lie Theory mathscidoc: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.
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  title={Normal subgroups in the Cremona group},
  author={Serge Cantat, Stéphane Lamy, and Yves de Cornulier},
  booktitle={Acta Mathematica},
Serge Cantat, Stéphane Lamy, and Yves de Cornulier. Normal subgroups in the Cremona group. 2010. Vol. 210. In Acta Mathematica. pp.31-94.
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