Three plots about the Cremona groups

Abstract

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other groups. The third concerns the connectedness of the Cremona groups.

28 pages. Theorems 2.14, 3.12, and Corollary 3.14 replaced by the more general statements, Corollaries 3.15, 3.16, 3.17 added, the list of references updated accordingly. Statement numbering changed. Accepted for publication in Izvestiya Mathematics