Rank 3 arithmetically Cohen-Macaulay bundles on hypersurfaces

Abstract

Let $X$ be a smooth projective hypersurface of dimension $\ge 5$ and let $E$ be an arithmetically Cohen-Macaulay bundle on $X$ of any rank. We prove that $E$ splits as a direct sum of line bundles if and only if $H_{\ast }^i(X,{\wedge }^{2}E)=0$ for $i=1,2,3,4$. As a corollary this result proves a conjecture of Buchweitz, Greuel and Schreyer for the case of rank 3 arithmetically Cohen-Macaulay bundles.