Jump of Milnor numbers (Q2462266)

In this article, the author studies the behaviour of the Milnor number in a 1-parameter deformation of an analytic germ of an isolated plane curve singularity. More precisely, he is interested in the smallest possible non-zero difference \(\lambda(f_0)=\mu(f_0)-\mu(f_s)\) for all possible deformations, where \(s\) denotes the deformation parameter. In particular, he shows (in a different way than S. Gusein-Zade) that considering 1-parameter deformations of an irreducible, Newton-nondegenerate plane curve singularity, this invariant is 1. To this end, he first considers only deformations in which all fibres (except \(f_0\)) are Newton-nondegenerate and establishes a characterization of the smallest difference of Milnor numbers for these deformations.