Rank-two weak Fano bundles on a four-dimensional quadric hypersurface $Q^4$

Abstract

We classify rank $2$ weak Fano bundles on a four-dimensional smooth quadric hypersurface $Q^4$. Up to twisting with a line bundle, such a bundle is either a split bundle, a spinor bundle, or one of the stable bundles with Chern classes $c_1=-1$ and $c_2=(1,1)$ constructed in [APW94].