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Quotient complete intersections of affine spaces by finite linear groups

Published online by Cambridge University Press:  22 January 2016

Haruhisa Nakajima
Haruhisa Nakajima*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya-ku, Tokyo 158, Japan
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Let G be a finite subgroup of GLn(C) acting naturally on an affine space Cn of dimension n over the complex number field C and denote by Cn/G the quotient variety of Cn under this action of G. The purpose of this paper is to determine G completely such that Cn/G is a complete intersection (abbrev. CI.) i.e. its coordinate ring is a C.I. when n > 10. Our main result is (5.1). Since the subgroup N generated by all pseudo-reflections in G is a normal subgroup of G and Cn/G is obtained as the quotient variety of without loss of generality, we may assume that G is a subgroup of SLn(C) (cf. [6, 16, 24, 25]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 98 , June 1985 , pp. 1 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

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