Castelnuovo-Mumford regularity of deficiency modules

Details Castelnuovo-Mumford regularity of deficiency modules Castelnuovo-Mumford regularity of deficiency modules

2009-01-06

arxiv.org/abs/0901.0690v3

Mathematics

Commutative Algebra

25 pages, the previous version divided in two parts

Scientific paper

Let $d \in \N$ and let $M$ be a finitely generated graded module of dimension $\leq d$ over a Noetherian homogeneous ring $R$ with local Artinian base ring $R_0$. Let $\beg(M)$, $\gendeg(M)$ and $\reg(M)$ respectively denote the beginning, the generating degree and the Castelnuovo-Mumford regularity of $M$. If $i \in \N_0$ and $n \in Z$, let $d^i_M(n)$ denote the $R_0$-length of the $n$-th graded component of the $i$-th $R_+$-transform module $D^i_{R_+}(M)$ of $M$ and let $K^i(M)$ denote the $i$-th deficiency module of $M$. Our main result says, that $\reg(K^i(M))$ is bounded in terms of $\beg(M)$ and the "diagonal values" $d^j_M(-j)$ with $j = 0,..., d-1$. As an application of this we get a number of further bounding results for $\reg(K^i(M))$.

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