Sequences of Milnor numbers of deformations of semi-quasi-homogeneous plane curve singularities
Volume 135 / 2025
Annales Polonici Mathematici 135 (2025), 251-263
MSC: Primary 14B07; Secondary 14N10, 32S30
DOI: 10.4064/ap241129-10-12
Published online: 10 January 2026
Abstract
Consider a semi-quasi-homogeneous complex plane curve singularity $f$ with Milnor number $\mu(f)$. In Theorem 1.1 we list integers which can be attained as Milnor numbers of deformations of the given semi-quasi-homogeneous singularity. The result follows mainly from combinatorial considerations and geometric interpretation of Euclid’s algorithm via the classic relation between Milnor and Newton numbers.
