Extremal Point Sets and Gorenstein Ideals

Abstract

The Hilbert function of a homogeneous ideal in R=k[x0 , ..., xn], k a field, is a much studied object. This is not surprising since the Hilbert function encodes important algebraic, combinatorial, and geometric information about the ideal. The fact that recent computer algebra developments have made the Hilbert function computable has not only sustained interest in them but sparked interest in many new questions about them. In this paper, we will concentrate on the Hilbert functions which are the Hilbert functions of points in P. From [11], we know that this is the same as studying 0-dimensional differentiable O-sequences (equivalently, the Hilbert functions of graded artinian quotients of k[x1 , ..., xn]). In our earlier paper [9], we began a discussion of n-type vectors and showed that they were in 1 1 correspondence with Hilbert functions of doi:10.1006 aima.1998.1889, available online at http: www.idealibrary.com on