\(T^ n\)-actions on holomorphically separable complex manifolds
type: Item
instance of: scholarly article
title: \(T^ n\)-actions on holomorphically separable complex manifolds
zbMATH Open document ID: 0651.32007
DOI: 10.1007/BF01180684
author: David E. Barrett
author: Eric Bedford
author: Jiri Dadok
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174076
review text: We study holomorphically separable n-dimensional complex manifolds M equipped with an effective \(T^ n\)-action. Our results relate the possibility of realizing M concretely as a Reinhardt domain or as an open subset of a toroidal embedding to various function-theoretic properties, such as the existence of a suitable envelope of holomorphy for M. Our method involves the study of a certain semigroup which is related to the Fourier expansion of holomorphic functions on M as well as to the isotropy subgroups for the group action. Our methods give rise in particular to new examples of (three- dimensional) holomorphically separable complex manifolds M for which \({\mathcal O}(M)\) is not a Stein algebra. (The first such example is due to Grauert.)
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32D10
zbMATH DE Number: 4061630
zbMATH Keywords: complex manifolds with a group action
zbMATH Keywords: envelope of holomorphy
MaRDI profile type: Publication
cites work: Q5658847
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description: scientific article; zbMATH DE number 4061630