1. ACM sets of points in multiprojective space
- Author
-
Elena Guardo and Adam Van Tuyl
- Subjects
Discrete mathematics ,Hilbert series and Hilbert polynomial ,13H10, 14M05, 13D40, 13D02 ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,16. Peace & justice ,Space (mathematics) ,01 natural sciences ,Set (abstract data type) ,Mathematics - Algebraic Geometry ,symbols.namesake ,0103 physical sciences ,FOS: Mathematics ,symbols ,010307 mathematical physics ,0101 mathematics ,Algebra over a field ,Algebraic Geometry (math.AG) ,Finite set ,Resolution (algebra) ,Mathematics - 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., 21 pages; revised final version; minor corrections; to appear in Collectanea Mathematica
- Published
- 2008