2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149970In this paper we find an algorithm which computes the Hilbert function of schemes $Z$ of "fat points" in $\PP3$ whose support lies on a rational normal cubic curve $C$. The algorithm shows that the maximality of the Hilbert function in degree $t$ is related to the existence of fixed curves (either $C$ itself or one of its secant lines) for the linear system of surfaces of degree $t$ containing $Z$.20 pages, plain TEX, no figuresAlgebraic Geometrytext