Castelnuovo-Mumford regularity, postulation numbers and relation types

JOURNAL OF ALGEBRA

卷:419

Article

Brodmann, Markus¹  Cao Huy Linh² 

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[2] Hue Univ, Coll Educ, Dept Math, Hue, Vietnam

关键词: Associated graded rings;    Castelnuovo-Mumford regularity;    Postulation number;    Relation type;    Uniform bound;   

DOI  :  10.1016/j.jalgebra.2014.07.014

来源: Elsevier

【 摘 要 】

We establish a bound for the Castelnuovo-Mumford regularity of the associated graded ring G(I) (A) of an m-primary ideal I of a local Noetherian ring (A, m) in terms of the dimension of A, the relation type and the number of generators of I. As a consequence, we obtain that the existence of uniform bounds for the regularity of the associated graded ring, and the relation type of parameter ideals in A, are equivalent conditions. In addition, we establish an equation for the postulation number and the Castelnuovo-Mumford regularity of the associated graded ring G(q) (A) of a parameter ideal q, which holds under certain conditions on the depths of the occurring rings. We also show, that the regularity of the ring G(q) (A) is bounded in terms of the dimension of A, the length of A/q and the postulation number of G(q) (A). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free