Rank 2 arithmetically Cohen-Macaulay bundles on a nonsingular cubic surface
Let \((X,L)\) be a polarized projective variety. A vector bundle \(E\) on \(X\) is called arithmetically Cohen-Macaulay (or ACM for short) if \(H^i(X, E\otimes L^n)=0\) for all integers \(n\) and \(0<i<\dim X\). These bundles have been the focus of intense study. In this paper the author studies rank 2 ACM bundles on cubic hypersurfaces in projective 3-space. Like Lefschetz theorem for line bundles on hypersurfaces, rank two ACM bundles are rare in higher dimensions. But for hypersurfaces in \({\mathbb P}^3\), these are ubiquitous. The author classifies these vector bundles on cubic hypersurfaces.
arithmetically Cohen-Macaulay vector bundles
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