Local and global results on the desingularization of three-dimensional vector fields. (English) Zbl 0645.14005

Singularités d’équations différentielles, Journ. Dijon/France 1985, Astérisque 150/151, 15-58 (1987).
[For the entire collection see Zbl 0623.00011.]
We present some local and global results concerning the desingularization of vector fields by means of blowing-ups of the ambient space (supposed of dimension three). The local reduction has been made in an earlier work and here we present with complete proofs the globalization of the local algorithm for a special kind of vector fields: those which have a “true” strict tangent space or directrix.


14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14J30 \(3\)-folds
14B05 Singularities in algebraic geometry


Zbl 0623.00011