We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially (ℙ1)n. A combinatorial characterization, the (⋆)-property, is known in ℙ1× ℙ1. We propose a combinatorial property, (⋆s) with 2 ≤ s ≤ n, that directly generalizes the (⋆)-property to (ℙ1)nfor 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, G.; Guardo, E.; Migliore, J.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 146:7(2018), pp. 2811-2825. [10.1090/proc/13981]
On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces
Favacchio G.;
2018
Abstract
We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially (ℙ1)n. A combinatorial characterization, the (⋆)-property, is known in ℙ1× ℙ1. We propose a combinatorial property, (⋆s) with 2 ≤ s ≤ n, that directly generalizes the (⋆)-property to (ℙ1)nfor 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.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2859444