Finite groups of polynomials automorphisms in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Finite groups of polynomials automorphisms in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0567.32010
author: M. Furushima
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1983-01-01T00:00:00Z
review text: For G a finite group of polynomial automorphisms of \({\mathbb{C}}^ n\) the author shows that there is a nonsingular algebraic compactification \(\iota\) : \({\mathbb{C}}^ n\to X\) with \(A=X-\iota ({\mathbb{C}}^ n)\) such that \(G=\iota^{-1}\circ \hat G\circ \iota\) for a finite subgroup \(\hat G\) of birational and biregular automorphisms of X which stabilize A. The leads to another proof [see e.g. the author, Mem. Fac. Sci., Kyushu Univ., Ser. A 36, 85-105 (1982; Zbl 0547.32015) and 37, 45-56 (1983; Zbl 0547.32016)], of the fact that for \(n=2\) such a G is conjugate to a subgroup of GL(2,\({\mathbb{C}})\). The author also shows that for \(n=3\), if X is the quadric, then G is conjugate to a subgroup of GL(3,\({\mathbb{C}})\).
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 3904958
zbMATH Keywords: characterization of finite group of polynomial automorphisms
zbMATH Keywords: algebraic compactification
reviewed by: Bruce Gilligan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178229000
OpenAlex ID: W2010332321
cites work: Compactifications of C n
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DOI: 10.2748/TMJ/1178229000
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description: scientific article; zbMATH DE number 3904958