Computing minimal generators of ideals of elliptic curves

In this paper results about the Hilbert function and about the number of minimal generators stated in (Orecchia) for disjoint unions of rational smooth curves are generalized to disjoint unions of distinct smooth non special curves, Hence, the maximal rank and the minimal generation of such curves are studied. In particular, we consider elliptic curves and we describe a method to compute their Hilbert functions in any dimension and for every choice of the degrees. Applications to the study of elliptic curves on threefolds are shown.