ACM bundles on general hypersurfaces in $\mathbb {P}^5$ of low degree

In this paper we show that on a general hypersurface of degree $r$ = 3, 4, 5, 6 in $\mathbb{P}^5$ a rank 2 vector bundle $\mathcal{E}$ splits if and only if $h^1\mathcal{E}(n) = h^2\mathcal{E}(n) = 0$ for all $n\in\mathbb{Z}$. Similar results for $r$ = 1, 2 were obtained in [15], [16] and [2].