On the Resolution of Ideals of Fat Points

In this paper we determine the Hilbert function and the minimal system of generators of r + 1 ≤ n + 1 general fat points of n. Furthermore, by looking at the minimal system of generators we can show that the ideal associated to two fat points in n or the ideal associated to r + 1 ≤ n general fat points, all with the same multiplicities, is a splittable ideal, and this is the first step in constructing a minimal resolution.