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.

Continuous automorphisms of Cremona groups

“…It could be interesting to generalize Déserti's theorem as well as the results of this paper to more general fields, in particular to finite fields. Another natural question is in as far similar results hold if we drop either the condition of surjectivity or injectivity of the group endomorphisms; these questions have been raised in [11], [18], and also [4].…”