Tame Loci of Certain Local Cohomology Modules

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 ${\text{ft}}^i(M{)}^{\le 3}$ at level $i \in $\mathbb{N}$0$incodimension$\leq 3$of$M$,thatisthesetsofallprimes$\fp_0 \subset R_0$ofheight$\leq 3$suchthatthegraded$R{\fp_0}$-modules$H^i_{R_{+}}(M)_{\fp_0}$ are tame.