Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- 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
On automorphism groups of affine surfaces
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.
Received: 28 November 2015
Revised: 1 August 2016
First available in Project Euclid: 21 September 2018
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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