Quotient singularities which are complete intersections
Let \(S={\mathbb{C}}[X_ 1,...,X_ n]\). Combined with his earlier results elsewhere the author completes in this paper the classification of all finite subgroups G of GL(n,\({\mathbb{C}})\) for which \(S^ G\) is a complete intersection (C.I.). The classification depends upon the following results of the author and others: (1) One may assume that \(G\subseteq SL(n,{\mathbb{C}})\); (2) if \(S^ G\) is a C.I. then \(S^ G\) is generated as a \({\mathbb{C}}\)-algebra by 2n-1 elements; (3) if \(S^ G\) is a C.I. then G is generated by \(\{g\in G| rank(g-id)\leq 2\};\) (4) if \(S^ G\) is a C.I. then for every homogeneous linear \(v\in S\), \(S^ H\) is a C.I., where H is the isotropy group of v in G.
action of subgroups of general linear group
scientific article; zbMATH DE number 3922861
scientific article