In this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for P1 × P1 and, more recently, in (P1)^r . In P1 × P1 the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in P m × P n . In such an ambient space it is equivalent to the so-called (∗)-property. Moreover, we start an investigation of the ACM property in P1 × Pn . We give a new construction that highlights how different the behavior of the ACM property is in this setting.

Multiprojective spaces and the arithmetically Cohen-Macaulay property / Favacchio, G.; Migliore, J.. - In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. - ISSN 0305-0041. - STAMPA. - 166:3(2019), pp. 583-597. [10.1017/S0305004118000142]

Multiprojective spaces and the arithmetically Cohen-Macaulay property

Favacchio G.;
2019

Abstract

In this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for P1 × P1 and, more recently, in (P1)^r . In P1 × P1 the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in P m × P n . In such an ambient space it is equivalent to the so-called (∗)-property. Moreover, we start an investigation of the ACM property in P1 × Pn . We give a new construction that highlights how different the behavior of the ACM property is in this setting.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2859718