Construction of low rank vector bundles on P⁴ and P⁵

Abstract

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P⁵. In characteristic p, we obtain rank two bundles on P⁴ and rank three bundles on P⁵. In arbitrary characteristic, we obtain rank three bundles on P⁴ and rank two bundles on the quadric S₅ in P⁶.