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Algebras of invariants of forms that are complete intersections. (English. Russian original) Zbl 0582.14019
Math. USSR, Izv. 23, 423-429 (1984); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 47, No. 6, 1155-1161 (1983).
Let \(G\to GL(V)\) be the representation of a reductive algebraic group over the field \({\mathbb{C}}\) and V/G be the affine algebraic manifold with ring of regular functions \({\mathbb{C}}[V]^ G\). The paper proves that V/G is a complete intersection in the case when \(G=SL(n)\) and \(V=S^ r({\mathbb{C}}^ n)\), if and only if when (n,r) is one of the following pairs (2,3), (2,4), (2,5), (2,6), (3,3), (4,3).
Reviewer: A.G.Elashvili

14M10 Complete intersections
14L24 Geometric invariant theory
14L30 Group actions on varieties or schemes (quotients)
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