English

ACM sets of points in multiprojective space

Commutative Algebra 2007-11-28 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0707.3138,
  title  = {ACM sets of points in multiprojective space},
  author = {Elena Guardo and Adam Van Tuyl},
  journal= {arXiv preprint arXiv:0707.3138},
  year   = {2007}
}

Comments

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

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