Holomorphic foliations and Kupka singular sets
type: Item
instance of: scholarly article
title: Holomorphic foliations and Kupka singular sets
zbMATH Open document ID: 0939.32029
author: Bruno Scárdua
author: César Camacho
published in: Communications in Analysis and Geometry
publication date: 2000-07-05T00:00:00Z
review text: Let \({\mathcal F}\) be a holomorphic codimension one foliation on a complex manifold \(M\) with the singularity \(\text{sing}({\mathcal F})\). The authors investigate the structure on the neighborhood of \(\text{sing} ({\mathcal F})\). After recalling the definition of the Kupka subset \(K({\mathcal F})\) of \(\text{sing}({\mathcal F})\) and summarizing the main properties of the Kupka subsets, the authors give some conditions for \({\mathcal F}\) to have an affine transverse or a projective transverse structure for \({\mathcal F}\) in a neighborhood of \(K({\mathcal F})\). The conditions are given by geometric properties for certain codimension 2 analytic subset \(S\) in \(\text{sing} ({\mathcal F})\).
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 1339901
zbMATH Keywords: holomorphic foliations
zbMATH Keywords: Kupka singular sets
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
DOI: 10.4310/CAG.1999.V7.N3.A6
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description: scientific article; zbMATH DE number 1339901