Normal subgroups in the Cremona group

Serge Cantat (1) , Stéphane Lamy (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k 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 which generate non trivial normal subgroups.

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Serge Cantat, Stéphane Lamy. Normal subgroups in the Cremona group. Acta Mathematica, 2013, 210 (1), pp.31-94. ⟨10.1007/s11511-013-0090-1⟩. ⟨hal-00705299⟩