The border of the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k}

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dc.creatorVan Tuyl, Adam
dc.date2001-12-18
dc.date.accessioned2026-07-07T04:45:19Z
dc.date.available2026-07-07T04:45:19Z
dc.descriptionWe describe the eventual behaviour of the Hilbert function of a set of distinct points in P^{n_1} x ... x P^{n_k}. As a consequence of this result, we show that the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k} 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.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0112185
dc.identifierhttp://arxiv.org/abs/math/0112185
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62911
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject13D40 (Primary) 05A17 14M05 (Secondary)
dc.titleThe border of the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k}
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