Milnor numbers of deformations of semi-quasi-homogeneous plane curve singularities

Abstract

The aim of this paper is to show the possible Milnor numbers of deformations of semi-quasi-homogeneous isolated plane curve singularities. Main result states that if $f$ is irreducible and nondegenerate, by deforming $f$ one can attain all Milnor numbers ranging from $\mu (f)$ to $\mu (f)-r(p-r)$, where $r$ and $p$ are easily computed from the Newton diagram of $f$.