Distribution of critical values of miniversal deformations of parabolic singularities (Q1066320)

In this paper the critical value mapping is considered, which associates with any polynomial from underdiagonal miniversal deformation of the family of parabolic singularities the set of its critical values. It is shown that the restriction of this mapping to the subset of polynomials with \(k\) different critical values, \(k\geq 2\), is a covering of the space of unordered \(k\)-tuples of different complex numbers. In particular, it is proved that the connected components of such subsets are \(K[\pi,1]\) spaces.