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Let $C$ be a projective plane curve of degree $d$ whose singularities are allisolated. Suppose $C$ is not concurrent lines. P{\l}oski proved that the Milnornumber of an isolated singlar point of $C$ is less than or equal to$(d-1)^{2}-\lfloor \frac{d}{2} \rfloor$. In this paper, we prove that theMilnor sum of $C$ is also less than or equal to $(d-1)^{2}-\lfloor \frac{d}{2}\rfloor$ and the equality holds if and only if $C$ is a P{\l}oski curve.Furthermore, we find a bound for the Milnor sum of projective plane curves interms of GIT.

A bound for the Milnor sum of projective plane curves in terms of GIT