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Normal subgroups in the Cremona group

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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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Correspondence to Serge Cantat.

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With an appendix by Yves de Cornulier.

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Cantat, S., Lamy, S. & de Cornulier, Y. Normal subgroups in the Cremona group. Acta Math 210, 31–94 (2013).

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