Please use this identifier to cite or link to this item:
Scopus Web of Science® Altmetric
Type: Journal article
Title: Sufficient conditions for holomorphic linearisation
Author: Kutzschebauch, F.
Larusson, F.
Schwarz, G.
Citation: Transformation Groups, 2016; 22(2):475-485
Publisher: Springer
Issue Date: 2016
ISSN: 1531-586X
Statement of
Frank Kutzschebauch, Finnur Lárusson, Gerald W. Schwarz
Abstract: Let G be a reductive complex Lie group acting holomorphically on X = ℂn. The (holomorphic) Linearisation Problem asks if there is a holomorphic change of coordinates on ℂn such that the G-action becomes linear. Equivalently, is there a G-equivariant biholomorphism Φ: X → V where V is a G-module? There is an intrinsic stratification of the categorical quotient QX, called the Luna stratification, where the strata are labeled by isomorphism classes of representations of reductive subgroups of G. Suppose that there is a Φ as above. Then Φ induces a biholomorphism φ: QX → QV which is stratified, i.e., the stratum of QX with a given label is sent isomorphically to the stratum of QV with the same label. The counterexamples to the Linearisation Problem construct an action of G such that QX is not stratified biholomorphic to any QV.Our main theorem shows that, for most X, a stratified biholomorphism of QX to some QV is sufficient for linearisation. In fact, we do not have to assume that X is biholomorphic to ℂn, only that X is a Stein manifold.
Rights: © Springer Science+Business Media New York (2016)
DOI: 10.1007/s00031-016-9376-7
Grant ID:
Appears in Collections:Aurora harvest 3
Mathematical Sciences publications

Files in This Item:
File Description SizeFormat 
  Restricted Access
Restricted Access200.43 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.