On automorphism groups of affine surfaces
Abstract
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.
Cite
@article{arxiv.1511.09051,
title = {On automorphism groups of affine surfaces},
author = {Sergei Kovalenko and Alexander Perepechko and Mikhail Zaidenberg},
journal= {arXiv preprint arXiv:1511.09051},
year = {2025}
}
Comments
Proposition 2.10 from the previous version (published in Algebraic Varieties and Automorphism Groups, ASPM 75) deleted. There is a mistake in the proof kindly indicated by J.-P. Furter; the validity of the result remains open. This does not affect the rest of the paper