%0 Journal Article
%A Arrondo Esteban, Enrique
%A Costa, Laura
%T Vector bundles on fano 3-folds without intermediate cohomology
%D 2000
%@ 0092-7872
%U https://hdl.handle.net/20.500.14352/57164
%X A well known result of G. Horrocks [Proc. Lond. Math. Soc. (3) 14, 689-713 (1964;Zbl 0126.16801)] says that a vector bundle on a projective space has no intermediatecohomology if and only if it decomposes as a direct sum of line bundles. It is also knownthat only on projective spaces and quadrics there is, up to a twist by a line bundle,a finite number of indecomposable vector bundles with no intermediate cohomology[see R.-O. Buchweitz, G.-M. Greuel and F.-O. Schreyer, Invent. Math. 88, 165-182(1987; Zbl 0617.14034) and also H. Kn¨orrer, Invent. Math. 88, 153-164 (1987; Zbl0617.14033)].In the paper under review the authors deal with vector bundles without intermediatecohomology on some Fano 3-folds with second Betti number b2 = 1. The Fano 3-foldsthey consider are smooth cubics in P4, smooth complete intersection of type (2, 2) in P5and smooth 3-dimensional linear sections of G(1, 4)  P9. A complete classification ofrank two vector bundles without intermediate cohomology on such 3-folds is given. Infact the authors prove that, up to a twist, there are only three indecomposable vectorbundles without intermediate cohomology. Vector bundles of rank greater than two arealso considered. Under an additional technical condition, the authors characterize thepossible Chern classes of such vector bundles without intermediate cohomology.
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