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.