Topologies and structures of the Cremona groups

• 成果类型: Article
• 署名作者: Blanc, Jeremy; Furter, Jean-Philippe
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.3.8
• 发表日期: 2013
• 页码: 1173-1198
• 关键词: pro-affine algebras; projective-space

摘要

We study the algebraic structure of the n-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (id-group) if n >= 2. We describe the obstruction to this, which is of a topological nature. By contrast, we show the existence of a Euclidean topology on the Cremona group which extends that of its classical subgroups and makes it a topological group.