Complete algebraic vector fields on affine surfaces. I
type: Item
instance of: scholarly article
title: Complete algebraic vector fields on affine surfaces. I
zbMATH Open document ID: 1061.32024
DOI: 10.1007/BF02921884
author: Julio C. Rebelo
published in: The Journal of Geometric Analysis
publication date: 2004-05-18T00:00:00Z
review text: The author studies holomorphic vector fields on an algebraic affine surface \(M\). Such a vector field is complete if it is `tangent' to a holomorphic flow \(M \times C \to M\). The singularities at infinity of the associated foliation are classified under mild assumptions. A sufficent condition is shown on these singularities that ensures the existence of the meromorphic first integral of the foliation. A special case of the result recovers a part of \textit{M. Brunella}'s [Topology 43, No.~2, 433--445 (2004; Zbl 1047.32015)] classification of complete polynomial vector fields on the complex plane.
reviewed by: Richárd Rimányi
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32M25
zbMATH DE Number: 2064457
zbMATH Keywords: singular foliation
zbMATH Keywords: complete vector field
zbMATH Keywords: singularity at infinity
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921884
OpenAlex ID: W2054678027
description: scientific article; zbMATH DE number 2064457