ACM sets of points in multiprojective space

Details ACM sets of points in multiprojective space ACM sets of points in multiprojective space

2007-07-20

arxiv.org/abs/0707.3138v2

Mathematics

Commutative Algebra

21 pages; revised final version; minor corrections; to appear in Collectanea Mathematica

Scientific paper

If X is a finite set of points in a multiprojective space P^n1 x ... x P^nr with r >= 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For sets of points in P^1 x P^1 there are several classifications of the ACM sets of points. In this paper we investigate the natural generalizations of these classifications to an arbitrary multiprojective space. We show that each classification for ACM points in P^1 x P^1 fails to extend to the general case. We also give some new necessary and sufficient conditions for a set of points to be ACM.

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