Group actions and envelopes of holomorphy
type: Item
instance of: scholarly article
title: Group actions and envelopes of holomorphy
zbMATH Open document ID: 0821.32009
DOI: 10.1007/BF01450511
author: Enrico Casadio Tarabusi
author: Stefano Trapani
published in: Mathematische Annalen
publication date: 1995-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/165277
review text: Suppose \(K\) is a compact Lie group and \(X\) is a Stein manifold on which \(K\) and its complexification \(K^{\mathbb{C}_ C}\) acts as groups of biholomorphic transformations. Assume \(\Omega\) is a \(K\)-invariant domain in \(X\). The present paper is concerned with the problem of determining the envelope of holomorphy \(E(\Omega)\) of \(\Omega\). Using results of \textit{D. Snow} [Math. Ann. 259, 79-97 (1982; Zbl 0509.32021)] and \textit{P. Heinzner} [Math. Ann. 289, No. 4, 631-662 (1991; Zbl 0728.32010)] the authors construct a Stein manifold \(U^*\) together with a holomorphic \(K^{\mathbb{C} c}\)-action such that \(E(\Omega)\) is schlicht and orbit convex in \(U^*\). Under some assumptions of a technical nature the approach of \textit{O. S. Rothaus} [Princeton Math. Ser. 31, P.U. Press, Princeton, 309- 317 (1970; Zbl 0212.108)], generalized to the present setting, is used to give an explicit description of the envelope of holomorphy as the interior of the zero set of a certain largest plurisubharmonic minorant.
reviewed by: Bruce Gilligan
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 734596
zbMATH Keywords: complexification of holomorphic actions
zbMATH Keywords: envelope of holomorphy
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 734596