Castelnuovo-Mumford Regularity and Cohomological Dimension

Let be a standard graded ring, be the irrelevant ideal of R and 0 be an ideal of R 0 . In this paper, as a generalization of the concept of Castelnouvo-Mumford regularity reg(M) of a finitely generated graded R-module M, we define the regularity of M with respect to 0  + R + , say reg 0  + R + (M)....

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Bibliographic Details
Published in:Communications in algebra 2014-01, Vol.42 (12), p.5454-5463
Main Author: Jahangiri, Maryam
Format: Article
Language:English
Subjects:
Algebra
Castelnouvo-Mumford regularity
Cohomological dimension
Invariants
Local cohomology
Regularity
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Summary:Let be a standard graded ring, be the irrelevant ideal of R and 0 be an ideal of R 0 . In this paper, as a generalization of the concept of Castelnouvo-Mumford regularity reg(M) of a finitely generated graded R-module M, we define the regularity of M with respect to 0  + R + , say reg 0  + R + (M). We also study some relations of this new invariant with the classic one. To this end, we need to consider the cohomological dimension of some finitely generated R 0 -modules. Also, we will express reg 0  + R + (M) in terms of some invariants of the minimal graded free resolution of M and see that in a special case this invariant is independent of the choice of 0 .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.788187