Abstract
We generalize the theory of Horrocks monads to ACM varieties, and use the generalization to establish a cohomological characterization of linear and Steiner bundles on projective space and on quadric hypersurfaces. We also characterize Steiner bundles on the Grassmannian G(1, 4) of lines in ℙ4. Finally, we study linear resolutions of bundles on ACM varieties, and characterize linear homological dimension on quadric hypersurfaces.
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