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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 $$ f = \sum _{q\alpha + p\beta \ \ge \ pq}c_{\alpha \beta }\ x^{\alpha }y^{\beta } $$f=∑qα+pβ≥pqcαβxαyβ where $$c_{p0}c_{0q}\ne 0$$cp0c0q≠0, $$2\le p<q$$2≤p<q and p, q are coprime. We show that as Milnor numbers of deformations of f one can attain all numbers from $$\mu (f)$$μ(f) to $$\mu (f)-r(p-r)$$μ(f)-r(p-r), where $$q\equiv r (\mathrm{mod\ }p)$$q≡r(modp). Moreover, we provide an algorithm which produces the desired deformations.

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