The border of the Hilbert function of a set of points in Pn1 x ••• x Pnk

[摘要] We describe the eventual behaviour of the Hilbert function of a set of distinct points in P-n1 x... x P-nk. As a consequence of this result, we show that the Hilbert function of a set of points in P-n1 X... X P-nk can be determined by computing the Hilbert function at only a finite number of values. Our result extends the result that the Hilbert function of a set of points in P-n stabilizes at the cardinality of the set of points. Motivated by our result, we introduce the notion of the border of the Hilbert function of a set of points. By using the Gale-Ryser Theorem, a classical result about (0, 1)-matrices, we characterize all the possible borders for the Hilbert function of a set of distinct points in P-1 x P-1. (C) 2002 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-12-24