Distribution of critical values of miniversal deformations of parabolic singularities

Summary We consider, in this paper, the critical values mapping, which associates with any polynomial from underdiagonal miniversal deformation of the family of parabolic singularities, the set of its critical values. We showed that the restriction of this mapping to the subset of polynomials withk different critical values,k2, is a covering of the space of unorderedk-tuples of different complex numbers. In particular, it is proved that the connected components of such subsets areK(, 1) spaces.