Normal subgroups in the Cremona group

• 成果类型: Article
• 署名作者: Cantat, Serge; Lamy, Stephane; de Cornulier, Yves
• 署名单位: Universite de Rennes; University of Warwick; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0090-1
• 发表日期: 2013
• 页码: 31-94
• 关键词: automorphisms

摘要

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane 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.