Vector bundles on G(1,4) without intermediate cohomology

Abstract

It is a famous result due to G. Horrocks [Proc. Lond. Math. Soc. (3) 14, 689-713 (1964; Zbl 0126.16801)] that line bundles on a projective space are the only indecomposable vector bundles without intermediate cohomology. This fact generalizes to quadric and grassmannians if we add cohomological conditions. In this paper the case of G(1, 4) is studied completely, and a characterization-classification of vector bundles on it without intermediate cohomology is obtained.