Castelnuovo-Mumford regularity of deficiency modules

Abstract

Let View the MathML source and let M be a finitely generated graded module of dimension less-than-or-equals, slantd over a Noetherian homogeneous ring R with local Artinian base ring R0. Let beg(M), gendeg(M) and reg(M) respectively denote the beginning, the generating degree and the Castelnuovo–Mumford regularity of M. If View the MathML source and nset membership, variantZ, let View the MathML source denote the R0-length of the n-th graded component of the i-th R+-transform module View the MathML source of M and let Ki(M) denote the i-th deficiency module of M.

Our main result says, that reg(Ki(M)) is bounded in terms of beg(M) and the “diagonal values” View the MathML source with j=0,…,d−1. As an application of this we get a number of further bounding results for reg(Ki(M)).