Extremal properties of Hilbert functions

Abstract

Throughout this paper k will be a field, S k[x Xn] the polynomial ring over k in the variables x Xn, and Si the degree homogeneous component of S. For a homogeneous ideal I _c S we denote by li the degree component of I. If V c_ Sa is a vector space, then we let 8(V) 8(codim(V, Sd), d). When there is no danger of confusion we write codim V instead of codim(V, Sa). We denote by (V) the ideal generated by V. Throughout x will be a general element of S. Fix d and let V cc_ Sa be a subspace.