A formula for the core of certain strongly stable ideals

JOURNAL OF ALGEBRA

卷:347

Article

Smith, Bonnie

关键词: Cores;    Reductions;    Monomial ideals;    Strongly stable ideals;    Artin-Nagata properties;   

DOI  :  10.1016/j.jalgebra.2011.08.031

来源: Elsevier

【 摘 要 】

The core of an ideal is the intersection of all of its reductions. The core is a natural object to study from the point of view of blow-up algebras and integral closure; and it also has geometric significance coming, for example, from its connection to adjoint and multiplier ideals. In general, the core is difficult to describe explicitly. In this paper, we investigate a particular family of strongly stable ideals. We prove that ideals in this family satisfy an Artin-Nagata property, yet fail to satisfy other, stronger standard depth conditions. We then show that there is a surprisingly simple explicit formula for the core of these ideals. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free