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Bounds for the Castelnuovo-Mumford regularity


Brodmann, M; Götsch, T (2009). Bounds for the Castelnuovo-Mumford regularity. Journal of Commutative Algebra, 1(2):197-225.

Abstract

We extend the “linearly exponential” bound
for the Castelnuovo-Mumford regularity of a graded ideal
in a polynomial ring K[x1, . . . , xr] over a field (established by Galligo and Giusti in characteristic 0 and recently, by Caviglia-Sbarra for abitrary K) to graded submodules of a graded module over a homogeneous Cohen-Macaulay ring R = ⊕n≥0Rn with artinian local base ring R0. As an application we get a “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded R-module M in terms of the degrees which occur in a minimal free presentation of M.

Abstract

We extend the “linearly exponential” bound
for the Castelnuovo-Mumford regularity of a graded ideal
in a polynomial ring K[x1, . . . , xr] over a field (established by Galligo and Giusti in characteristic 0 and recently, by Caviglia-Sbarra for abitrary K) to graded submodules of a graded module over a homogeneous Cohen-Macaulay ring R = ⊕n≥0Rn with artinian local base ring R0. As an application we get a “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded R-module M in terms of the degrees which occur in a minimal free presentation of M.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:16 Nov 2009 21:22
Last Modified:05 Apr 2016 13:22
Publisher:Rocky Mountain Mathematics Consortium
ISSN:1939-2346
Publisher DOI:https://doi.org/10.1216/JCA-2009-1-2-197

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