Invariant plurisubharmonic exhaustions and retractions
type: Item
instance of: scholarly article
title: Invariant plurisubharmonic exhaustions and retractions
zbMATH Open document ID: 0842.32010
DOI: 10.1007/BF02567597
author: P. Heinzner
author: Alan Huckleberry
published in: Manuscripta Mathematica
publication date: 1994-07-04T00:00:00Z
full work available at URL: https://eudml.org/doc/155944
review text: Let \(X\) be a Stein manifold equipped with an \(R\)-analytic \(K \times X \to X\) of a compact Lie group \(K\) of holomorphic transformations. There is a \(K\)-invariant strictly plurisubharmonic exhaustion \(\phi\): \(X \to \mathbb{R}^+\) which plays the role of a norm. The Kempf-Ness set \(R = R(\phi)\) can be defined as the zero-set of the associated moment norm-function and the flow is associated to the Kähler-form \(i \ni \overline{\delta} \phi\). The authors modify \(\phi\) outside of its Kempf-Ness set \(R = R(\phi)\) so that the resulting gradient flow realizes \(R(\phi)\) as a strong deformation retract of \(X\). As a consequence, they derive topological results which are analogous to those in the algebraic case and apply to a local existence for equivalent structures on topological \(K\)-bundles, which is a necessary tool for the proof of the equivalent version of Oka-Grauert's principle. They also apply to a homotopically equivalent theorem of \(X\) and a universal Stein manifold \(X^c\) containing \(X\) as an open, Runge \(K\)-invariant subset.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 599661
zbMATH Keywords: retractions
zbMATH Keywords: plurisubharmonic exhaustion
reviewed by: J. Kajiwara
MaRDI profile type: Publication
cites work: On Levi's problem and the imbedding of real-analytic manifolds
cites work: Geometric invariant theory on Stein spaces
cites work: Equivariant holomorphic extensions of real analytic manifolds
cites work: Q4031236
cites work: An equivariant version of Grauert's Oka principle
cites work: Q3346437
cites work: Q4193681
cites work: Q3686804
cites work: Quotient varieties
cites work: The topology of quotient varieties
cites work: Reductive group actions on Stein spaces
description: scientific article; zbMATH DE number 599661