Splitting of low rank ACM bundles on hypersurfaces of high dimension

Abstract

Let $X$ be a smooth projective hypersurface. In this note we show that any rank 3 arithmetically Cohen-Macaulay vector bundle over $X$ splits when dim $X\ge 7$. We also find a splitting criterion for rank 4 arithmetically Cohen-Macaulay vector bundles on $X$ when dim $X\ge 9$.

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