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Multiprojective spaces and the arithmetically Cohen–Macaulay property
Published online by Cambridge University Press: 03 April 2018
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 ℙm × ℙn. 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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 3 , May 2019 , pp. 583 - 597
- Copyright
- Copyright © Cambridge Philosophical Society 2018
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