ACM sets of points in multiprojective sapce

Elena Guardo; Adam van Tuyl

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ACM sets of points in multiprojective sapce

Autores: Elena Guardo, Adam van Tuyl
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 2, 2008, págs. 191-213
Idioma: inglés
DOI: 10.1007/bf03191367
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Resumen
- IfXis a finite set of points in a multiprojective spacePn1×· · ·×Pnr with r 2, then X may or may not be arithmetically CohenMacaulay (ACM). For sets of points in P1 × 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 ×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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