On the graded resolution of few general fat points of P^n

We compute the graded Betti numbers of the ideal of ''few'' (at most n) fat points of P^n with support in general position, under the assumption that the multiplicities are all equal except one, which has to be at least twice as much. We do so by performing a sequence of splittings and applying the graded version given by Fatabbi of a result of Eliahou and Kervaire. In doing so, we also prove that the ideal of at most n general fat points of P^n is always splittable and we compute the graded Betti numbers of the product of two ideals whose generators involve disjoint sets of indeterminates.