Tame Loci of Certain Local Cohomology Modules

Abstract

Let $M$ be a finitely generated graded module over a Noetherian homogeneous ring $R={⨁}_{n\in {\mathbb{N}}_0}{R}_n$. For each $i\in {\mathbb{N}}_0$ let $H_{R_{+}}^i(M)$ denote the $i$-th local cohomology module of $M$ with respect to the irrelevant ideal $R_{+}={⨁}_{n>0}{R}_n$ of $R$, furnished with its natural grading. We study the tame loci $\ft^i(M)^{\leq 3}$ at level $i\in {\mathbb{N}}_0$ in codimension $\le 3$ of $M$, that is the sets of all primes $\fp_0 \subset R_0$ of height $\le 3$ such that the graded $R_{\fp_0}$-modules $H^i_{R_{+}}(M)_{\fp_0}$ are tame.

15 pages, to appear in Journal of Commutative Algebra