Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hilbert functions of ACM sets of points in P^{n_1} x ... x P^{n_k}   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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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas