Open Access
2013 Normal subgroups in the Cremona group
Serge Cantat, Stéphane Lamy, Yves Cornulier
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Acta Math. 210(1): 31-94 (2013). DOI: 10.1007/s11511-013-0090-1

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

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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

Information

Received: 7 July 2010; Revised: 20 May 2011; Published: 2013
First available in Project Euclid: 31 January 2017

zbMATH: 1278.14017
MathSciNet: MR3037611
Digital Object Identifier: 10.1007/s11511-013-0090-1

Rights: 2013 © Institut Mittag-Leffler

Vol.210 • No. 1 • 2013
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