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Deformations of reductive group actions

Published online by Cambridge University Press:  24 October 2008

Gerd Müller
Gerd Müller
Affiliation:
Fachbereich Mathematik, Universität Mainz, Saarstraβe 21, D-6500 Mainz, West Germany
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Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of actions on analytic ℂ-algebras, see Theorem 2 below. An analogue for actions on formal ℂ-algebras is given there too.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 77 - 88
Copyright
Copyright © Cambridge Philosophical Society 1989

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