On the Hilbert Function of Fat Points on a Rational Normal Cubic Original Research Article

In this paper we find an algorithm which computes the Hilbert function of schemesZof “fat points” in image3whose support lies on a rational normal cubic curveC. The algorithm shows that the maximality of the Hilbert function in degreetis related to the existence of fixed curves (eitherCitself or one of its secant lines) for the linear system of surfaces of degreetcontainingZ.