On \(\mathbb{C}\)-actions on compact complex manifolds with many compact orbits
type: Item
instance of: scholarly article
title: On \(\mathbb{C}\)-actions on compact complex manifolds with many compact orbits
zbMATH Open document ID: 0811.32027
DOI: 10.1007/BF02567688
author: Jörg Winkelmann
published in: Manuscripta Mathematica
publication date: 1995-05-02T00:00:00Z
full work available at URL: https://eudml.org/doc/155918
review text: The author proves the following theorem. Suppose \(X\) is a compact complex manifold which admits a holomorphic action of the Lie group \(G = (\mathbb{C},+)\) such that there is a \(G\)-invariant set \(\Omega \subset X\) of positive Lebesgue measure in which every \(G\)-orbit is compact. Then the \(G\)-action on \(X\) fibers through a torus action. This result was proved in the case \(\Omega = X\) by \textit{H. Holmann} [Comment. Math. Helv. 52, 251-257 (1977; Zbl 0353.32034)], and in the case \(X\) is Kähler a similar statement follows from the results of \textit{D. Snow} [Arch. Math. 37, 364-371 (1981; Zbl 0468.57030)]. The author also gives examples which show that the corresponding statements are false if one has a differentiable \(\mathbb{R}\)-action or if \(X\) is not compact.
reviewed by: Bruce Gilligan
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 554379
zbMATH Keywords: compact orbits
zbMATH Keywords: compact complex manifold
zbMATH Keywords: Lie group
MaRDI profile type: Publication
cites work: Q3997201
cites work: Analytische periodische Strömungen auf kompakten komplexen Räumen
OpenAlex ID: W2056915808
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description: scientific article; zbMATH DE number 554379