Оn automorphism groups of affine surfaces

Sergei Kovalenko (1) , Alexander Perepechko (2) , Mikhail Zaidenberg (3)

1 FRIAS - Freiburg Institute for Advanced Studies
2 SPbU - St Petersburg State University
3 IF - Institut Fourier

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic groups. At the same time, they can be studied from the viewpoint of the combinatorial group theory, so we put a special accent on group-theoretical aspects (ind-groups, amalgams, etc.). We provide different approaches to classification, prove certain new results, and attract attention to several open problems.

Mots clés: affine surface; automorphism group; affine fibration; amalgamated product; algebraic group; ind-group

Domaines: Géométrie algébrique [math.AG]

Sergei Kovalenko, Alexander Perepechko, Mikhail Zaidenberg. Оn automorphism groups of affine surfaces. 2015. ⟨hal-01235237v1⟩