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Multiprojective spaces and the arithmetically Cohen–Macaulay property

Published online by Cambridge University Press:  03 April 2018

GIUSEPPE FAVACCHIO  and
JUAN MIGLIORE
GIUSEPPE FAVACCHIO
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania Viale A. Doria, 6 – 95100 – Catania, Italy. e-mail: [email protected]
JUAN MIGLIORE
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, U.S.A. e-mail: [email protected]
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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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References

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