Vector Bundles on Fano 3-folds without Intermediate Cohomology

A well-known result of Horrocks (see [Ho]) states that a vector bundle on a projective space has not intermediate cohomology if and only if it decomposes as a direct sum of line bundles. There are two possible generalizations of this result to arbitrary varieties. The first one consists of giving a cohomological characterization of direct sums of line bundles. This has been done for quadrics and Grassmannians by Ottaviani (see [O1], [O2]) and for rank-two vector bundles on smooth hypersurfaces in P by Madonna (see [Ma]). The second generalization, to which we make some contribution in this paper, is to characterize vector bundles without intermediate cohomology. Besides the result of Horrocks for projective spaces, there is such a characterization for smooth quadrics due to Knörrer (see [Kn]). In fact, it was shown by Buchweitz, Greuel and Schreyer that only in the above two kind of varieties (projective spaces and quadrics) there is,