Advanced Studies in Pure Mathematics

On automorphism groups of affine surfaces

Sergei Kovalenko, Alexander Perepechko, and 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.

Article information

Source
Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 207-286

Dates
Received: 28 November 2015
Revised: 1 August 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537498711

Digital Object Identifier
doi:10.2969/aspm/07510207

Mathematical Reviews number (MathSciNet)
MR3793368

Zentralblatt MATH identifier
1396.14058

Subjects
Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R20: Group actions on affine varieties [See also 13A50, 14L30]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations

Keywords
Affine surface automorphism group group action amalgamated product

Citation

Kovalenko, Sergei; Perepechko, Alexander; Zaidenberg, Mikhail. On automorphism groups of affine surfaces. Algebraic Varieties and Automorphism Groups, 207--286, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510207. https://projecteuclid.org/euclid.aspm/1537498711


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