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The Hilbert functions of ACM sets of points in P^{n_1} x ... x P^{n_k}

Adam Van Tuyl
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Abstract

The Hilbert functions of sets of distinct points in P^n have been characterized. We show that if we restrict to sets of distinct of points in P^{n_1} x ... x P^{n_k} that are also arithmetically Cohen-Macaulay (ACM for short), then there is a natural generalization of this result. We begin by determining the possible values for the invariants K-dim R/Ix and depth R/Ix, where R/Ix is the coordinate ring associated to a set of distinct points X in P^{n_1} x ... x P^{n_k}. At the end of this paper we give a new characterization of ACM sets of points in P^1 x P^1.

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Adam Van Tuyl. 2003-02-25. The Hilbert functions of ACM sets of points in P^{n_1} x ... x P^{n_k}. https://arxiv.org/abs/math/0112186

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