The Border of the Hilbert Function of a Set of Points
نویسنده
چکیده
We describe the eventual behaviour of the Hilbert function of a set of distinct points in Pn1 × · · · × Pnk . As a consequence of this result, we show that the Hilbert function of a set of points in Pn1 × · · · × Pnk 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 Pn 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 × P.
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