  Let $X$ be a smooth Fano manifold equipped with a `` nice '' $n$-blocks
collection in the sense of \cite{cm2} and $\mathcal {F}$ a coherent sheaf on
$X$. Assume that $X$ is Fano and that all blocks are coherent sheaves. Here we
prove that $\mathcal {F}$ has regularity $-\infty$ in the sense of \cite{cm2}
if ${Supp}(\mathcal {F})$ is finite, the converse being true under mild
assumptions. The corresponding result is also true when $X$ has a geometric
collection in the sense of \cite{cm1}.
