The jump of the Milnor number of quasihomogeneous singularities for linear deformations

Abstract

The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformations $f_s$. We determinate the jump of quasihomogeneous singularities in the class of linear deformations.