Jumping conics on a smooth quadric in $${\mathbb {P}_3}$$

Abstract

We investigate the jumping conics of stable vector bundles E of rank 2 on a smooth quadric surface Q with the first Chern class \({c_1= \mathcal{O}_Q(-1,-1)}\) with respect to the ample line bundle \({\mathcal {O}_Q(1,1)}\) . We show that the set of jumping conics of E is a hypersurface of degree c 2(E) − 1 in \({\mathbb {P}_3^{*}}\) . Using these hypersurfaces, we describe moduli spaces of stable vector bundles of rank 2 on Q in the cases of lower c 2(E).