On the saturation sequence of the rational normal curve

Let denote the rational normal curve of order d. Its homogeneous defining ideal admits an SL2-stable filtration J2⊆J4⊆…⊆IC by sub-ideals such that the saturation of each J2q equals IC. Hence, one can associate to d a sequence of integers (α1,α2,…) which encodes the degrees in which the successive inclusions in this filtration become trivial. In this paper we establish several lower and upper bounds on the αq, using inter alia the methods of classical invariant theory.