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arXiv · 1511.09051

On automorphism groups of affine surfaces

Sergei Kovalenko·Alexander Perepechko·Mikhail Zaidenberg
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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.

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Sergei Kovalenko, Alexander Perepechko, Mikhail Zaidenberg. 2015-11-29. On automorphism groups of affine surfaces. https://doi.org/10.2969/aspm%2F07510207

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