Given a Schubert variety S contained in a Grassmannian Gk(Cl), we show how to obtain further information on the direct summands of the derived pushforward Rπ⁎QS˜ given by the application of the decomposition theorem to a suitable resolution of singularities π:S˜→S. As a by-product, Poincaré polynomial expressions are obtained along with an algorithm which computes the unknown terms in such expressions and which shows that the actual number of direct summands happens to be less than the number of supports of the decomposition.

We present an implementation of an algorithm for computing minimal homogeneous generators and Hilbert functions of ideals of fat points. First we construct a set of generators by an interpolating method which is based on the Hermite interpolation and generalizes the algorithm of [20] to projective space. Then, we minimalize the generators by the same algorithm which has been developed in [6] by exploiting results of [23] and [19] and which has been already successfully applied to ideals of points, to ideals of rational curves [3] and to ideals of general parametric varieties [22].