Degenerating families of rank two bundles

Abstract:

We construct families of rank two bundles $\mathcal {E}_t$ on $\mathbf {P}^4$, in characteristic two, where for $t\neq 0$, $\mathcal {E}_t$ is a sum of line bundles, and $\mathcal {E}_0$ is non-split. We construct families of rank two bundles $\mathcal {E}_t$ on $\mathbf {P}^3$, in characteristic $p$, where for $t\neq 0$, $\mathcal {E}_t$ is a sum of line bundles, and $\mathcal {E}_0$ is non-split.