On the classification of smooth compact \(\mathbb{C}^*\)-surfaces
type: Item
instance of: scholarly article
title: On the classification of smooth compact \(\mathbb{C}^*\)-surfaces
zbMATH Open document ID: 0830.32012
DOI: 10.1007/BF01446658
published in: Mathematische Annalen
publication date: 1995-06-27T00:00:00Z
full work available at URL: https://eudml.org/doc/165318
review text: The author classifies smooth compact complex surfaces with a nontrivial holomorphic \(\mathbb{C}^*\)-action possessing fixed points. He reduces the problem to minimal surfaces and proves the main result: The minimal surfaces as above belong to three classes: (i) algebraic surfaces, (ii) Hopf surfaces, (iii) parabolic Inoue surfaces. (The \(\mathbb{C}^*\)-actions are described by the author). He also gives the list of all the minimal compact almost homogeneous complex surfaces. These are: (i) minimal rational surfaces, (ii) topologically trivial \(\mathbb{P}_1\)-bundles over a one-dimensional complex torus, (iii) Hopf surfaces with an abelian fundamental group, (iv) two-dimensional complex tori.
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32M12
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 759293
zbMATH Keywords: group action
zbMATH Keywords: almost homogeneous complex manifold
zbMATH Keywords: minimal surface
author: Jürgen Hausen
reviewed by: Krzysztof Dabrowski
MaRDI profile type: Publication
cites work: Q5850167
cites work: Q5658847
cites work: Q4740820
cites work: Surfaces of class \(VII_ 0\) with curves
cites work: Komplexe Flächen mit holomorphen Vektorfeldern. (Complex surfaces with holomorphic vector fields)
cites work: Fixpunktmengen kompakter Gruppen in Teilgebieten Steinscher Mannigfaltigkeiten.
cites work: Geometric invariant theory on Stein spaces
cites work: On the Structure of Compact Complex Analytic Surfaces, II
cites work: On surfaces of class VII\(_ 0\) with curves
cites work: Algebraic surfaces with k*-action
cites work: On almost homogeneous compact complex analytic surfaces
cites work: Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten
cites work: Analytic compactifications of complex homology cells
OpenAlex ID: W2136274777
description: scientific article; zbMATH DE number 759293