The universal rank-(n-1) bundle on G(1,n) restricted to subvarieties

We classify those smooth (n-1)-folds in G(1,n) for which the restriction of the rank-(n-1) universal bundle has more than n+1 independent sections. As an aplication, we classify also those (n-1)-folds for which that bundle splits.Comment: 11 pages, plain te

A home-made Hartshorne-Serre correspondence

We provide an elementary proof of the Hartshorne-Serre correspondence for constructing vector bundles from local complete intersection subschemes of codimension two. This will be done, as in the correspondence of hypersurfaces and line bundles, by patching together local determinantal equations in order to produce sections of a vector bundle.Comment: 19 page

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

We characterize the vector bundles on G(1,4) that have no intermediate cohomology. We obtain them from extensions of the universal bundles and others related with them. In particular, we get a characterization of the universal vector bundles from their cohomology.Comment: 12 page