Realization of singular curves in dicritic foliations with prescribed involutions

Abstract The purpose of this work is to prove that any analytic class of germs of singular curves in ( C 2 , 0 ) having n + 1 pairwise transversal smooth branches can be realized in an appropriate dicritic foliation with prescribed collection of involutions. It is a step towards the thorough understanding of the geometry of the finite parametric (analytic) invariants of singular curves and singular foliations.