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Acta Mathematica

, Volume 210, Issue 1, pp 31–94 | Cite as

Normal subgroups in the Cremona group

  • Serge Cantat
  • Stéphane Lamy
  • Yves de Cornulier
Article

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.

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Copyright information

© Institut Mittag-Leffler 2013

Authors and Affiliations

  • Serge Cantat
    • 1
    • 2
  • Stéphane Lamy
    • 3
    • 4
  • Yves de Cornulier
    • 5
  1. 1.Université de Rennes IRennes CedexFrance
  2. 2.Département de Mathématiques et Appl.École Normale SupérieureParis Cedex 5France
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK
  4. 4.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouse Cedex 9France
  5. 5.Laboratoire de Mathématiques d’OrsayCNRS & Université Paris-Sud 11OrsayFrance

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