Finite groups of polynomials automorphisms in \({\mathbb{C}}^ n\)
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,\({\mathbb{C}})\).
characterization of finite group of polynomial automorphisms
scientific article; zbMATH DE number 3904958
scientific article