Milnor Numbers of Deformations of Semi-Quasi-Homogeneous Plane Curve Singularities

摘要

The aim of this paper is to show the possible Milnor numbers of deformations of semi-quasi-homogeneous isolated plane curve singularity f. Assuming that f is irreducible, one can write f = qa+ p ss = pq ca ss xa y ss where cp0c0q = 0, 2 = p < q and p, q are coprime. We show that as Milnor numbers of deformations of f one can attain all numbers from mu(f) to mu(f)-r (p-r), where q = r (mod p). Moreover, we provide an algorithm which produces the desired deformations.