Quotient singularities which are complete intersections
type: Item
instance of: scholarly article
title: Quotient singularities which are complete intersections
zbMATH Open document ID: 0577.14038
DOI: 10.1007/BF01169006
author: Haruhisa Nakajima
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155024
review text: 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.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14L24
zbMATH DE Number: 3922861
zbMATH Keywords: action of subgroups of general linear group
zbMATH Keywords: invariant space as
zbMATH Keywords: complete intersection
reviewed by: Balwant Singh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3922861