Absolutely isolated singularities of holomorphic vector fields
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.
scientific article; zbMATH DE number 4129187