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arXiv · 1305.5102

A bound for the Milnor number of plane curve singularities

Arkadiusz Płoski
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Abstract

Let $f=0$ be a plane algebraic curve of degree $d>1$ with an isolated singular point at the origin of the complex plane. We show that the Milnor number $μ_0(f)$ is less than or equal to $(d-1)^2-\left[\frac{d}{2}\right]$, unless $f=0$ is a set of $d$ concurrent lines passing through 0. Then we characterize the curves $f=0$ for which $μ_0(f)=(d-1)^2-\left[\frac{d}{2}\right]$.

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Arkadiusz Płoski. 2013-05-22. A bound for the Milnor number of plane curve singularities. https://arxiv.org/abs/1305.5102

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