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Quotient singularities which are complete intersections. (English) Zbl 0577.14038

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.
Reviewer: B.Singh

MSC:

14L30 Group actions on varieties or schemes (quotients)
14M10 Complete intersections
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
14B05 Singularities in algebraic geometry
14L24 Geometric invariant theory
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References:

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