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BOUNDS FOR THE CASTELNUOVO-MUMFORD REGULARITY

By M. Brodmann and Th. Götsch

Abstract

We extend the “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded ideal in a polynomial ring K[x1,...,xr] overafield(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

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.4775
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