A bound for the Milnor number of plane curve singularities

Original · EN

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 μ₀(f) is less than or equal to (d-1)²-[d/2], unless f=0 is a set of d concurrent lines passing through 0. Then we characterize the curves f=0 for which μ₀(f)=(d-1)²-[d/2].