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