ACM sets of points in multiprojective space

2007/07/20 by Elena Guardo, Guardo, Elena, Adam Van Tuyl +1 · 1 citation
Computer Science · Engineering · Mathematics · #13D02 #13D40 #13H10 #14M05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0707.3138

openalex publication_date 2007/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If X is a finite set of points in a multiprojective space Pⁿ1 x ... x Pⁿr with r >= 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For sets of points in P¹ x P¹ 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 P¹ x P¹ 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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• Separators of points in a multiprojective space

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