How do I show that a plane curve of degree d is unstable ( in the GIT sense ) if it has a singular point of multiplicity > 2d/3? This is an exercise from Dolgachev’s book Lectures on invariant theory ( chapter 10 ex 12 )
I’m supposed to choose a specific 1-PS $\lambda$ and use the Hilbert-Mumford criterion, but I do not have a good description of the singularities of a deg d $\geq$4 curve.