Absolutely isolated singularities of holomorphic vector fields
type: Item
instance of: scholarly article
title: Absolutely isolated singularities of holomorphic vector fields
zbMATH Open document ID: 0689.32008
DOI: 10.1007/BF01388858
author: Paulo Sad
author: César Camacho
author: Felipe Cano
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143734
review text: Let X be a \({\mathbb{C}}\)-manifold with \(\dim_{{\mathbb{C}}}X=n\) and let \({\mathcal D}\) be a singular analytic foliation by lines on X, let assume that the singular points of \({\mathcal D}\) consist of exactly one point say P. The authors want to find: a \({\mathbb{C}}\)-manifold M and a proper holomorphic map \(\Phi: M\to X\) such that \(\Phi^{-1}(P)\) is a union of codimension one compact \({\mathbb{C}}\)-submanifolds with normal crossings such that the pull back foliation \(\Phi\) *(\({\mathcal D}|_{X\setminus P})\) extends to a singular foliation of M with singular set of codimension \(\geq 2\) and such that all the singular points are irreducible. In the special case where the singular set of the lifted foliation has codimension \(=n\), the authors, among other things, solved this problem by a sequence of blow-ups.
Mathematics Subject Classification ID: 32Sxx
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 4129187
zbMATH Keywords: singular foliation
MaRDI profile type: Publication
cites work: Topological invariants and equidesingularization for holomorphic vector fields
cites work: Q3328651
cites work: Final forms for a three-dimensional vector field under blowing-up
cites work: Reduction of Singularities of the Differential Equation Ady = Bdx
OpenAlex ID: W2064151253
description: scientific article; zbMATH DE number 4129187