On the Saito number of plane curves

In this work we study the Saito number of a plane curve and we present a method to determine the minimal Saito number for plane curves in a given equisingularity class, that gives rise to an actual algorithm. In particular situations, we also provide various formulas for this number. In addition, if ν₀ and ν₁ are two coprime positive integers and $N>0$ then we show that for any 1≤ k≤ [Nν₀/2 ] there exits a plane curve equisingular to the curve yNν₀-xNν₁=0 such that its Saito number is precisely k.