Jordan groups and automorphism groups of algebraic varieties

Abstract

This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix is the expanded version of my notes on open problems posted on the site of this workshop. It contains formulations of some open problems and the relevant comments.

25 pages. Examples 3, 6, 16, Theorem 4, 6, Proposition 3, Remark 1, some comments in Sections 2.1, 2.3.4, 3.2, 3.3, 3.4, and several references are added

References in corpus (2)

• Groups acting on manifolds: around the Zimmer program
• On the Cayley degree of an algebraic group

Cited by in corpus (6)

• Jordan property for non-linear algebraic groups and projective varieties
• Finite subgroups of diffeomorphism groups
• Boosting an analogue of Jordan's theorem for finite groups
• p-subgroups in the space Cremona group
• Jordan constant for Cremona group of rank 3
• On Jordan type bounds for finite groups of diffeomorphisms of 3-manifolds and Euclidean spaces