Castelnuovo–Mumford regularity of deficiency modules

Let d∈N and let M be a finitely generated graded module of dimension ⩽d 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 i∈N0 and n∈Z, let denote the R0-length of the n-th graded component of the i-th R+-transform module 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” with j=0,…,d−1. As an application of this we get a number of further bounding results for reg(Ki(M)).