## On the topological triviality along moduli of deformations of $J_{k,0}$ singularities

### Volume 75 / 2000

Annales Polonici Mathematici 75 (2000), 193-212
DOI: 10.4064/ap-75-3-193-212

#### Abstract

It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J. Damon and A. Galligo, concerning the case of the Pham singularity ($J_{3,0}$ in Arnold's classification) (see [2, 3, 4]), and deal with deformations of general $J_{k,0}$ singularities.