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 P 5 \mathbf {P}^{5} . In characteristic p p , we obtain rank two bundles on P 4 \mathbf {P}^4 and rank three bundles on P 5 \mathbf {P}^5 . In arbitrary characteristic, we obtain rank three bundles on P 4 \mathbf {P}^4 and rank two bundles on the quadric S 5 S_5 in P 6 \mathbf {P}^6 .