Acta Mathematica

Normal subgroups in the Cremona group

Serge Cantat, Stéphane Lamy, and Yves Cornulier

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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.

Article information

Source
Acta Math., Volume 210, Number 1 (2013), 31-94.

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892672

Digital Object Identifier
doi:10.1007/s11511-013-0090-1

Mathematical Reviews number (MathSciNet)
MR3037611

Zentralblatt MATH identifier
1278.14017

Rights
2013 © Institut Mittag-Leffler

Citation

Cantat, Serge; Lamy, Stéphane; Cornulier, Yves. Normal subgroups in the Cremona group. Acta Math. 210 (2013), no. 1, 31--94. doi:10.1007/s11511-013-0090-1. https://projecteuclid.org/euclid.acta/1485892672


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