We study the arithmetically Cohen-Macaulay (ACM) property for finite setsof points in multiprojective spaces, especially (P_1)^n. A combinatorial characterization, the (⋆)-property, is known in P1 × P1. We propose a combinatorial property, (⋆n), thatdirectly generalizes the (⋆)-property to (P1^)n for larger n. We show that X is ACM if and only if it satisfies the (⋆n)-property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.

On the Arithmetically Cohen-Macaulay property for sets of points in Multiprojective Spaces

FAVACCHIO, GIUSEPPE;GUARDO, ELENA MARIA
;
2018-01-01

Abstract

We study the arithmetically Cohen-Macaulay (ACM) property for finite setsof points in multiprojective spaces, especially (P_1)^n. A combinatorial characterization, the (⋆)-property, is known in P1 × P1. We propose a combinatorial property, (⋆n), thatdirectly generalizes the (⋆)-property to (P1^)n for larger n. We show that X is ACM if and only if it satisfies the (⋆n)-property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.
2018
cohen- macaulay, multiprojective spaces, points
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/117870
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