Normal subgroups in the Cremona group

By Serge Cantat, St'ephane Lamy, Yves Cornulier. 2010

126 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1e5184f38685c179a7193744dc2ef96cb35dad90

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “8] in [41]).”
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings (2014, background): “Cantat and Lamy [45] proved that the Cremona group (i.”
Dynamics of automorphisms of compact complex surfaces (2014, background): “Moreover, the group Bir(X) acts on an infinite dimensional hyperbolic space H∞ and this classification into types can be explained in terms of elliptic, parabolic and loxodromic isometries; such a classification can then be used to study groups of birational transformations (see [30, 40]).”