A refined stable restriction theorem for vector bundles on quadric threefolds

Let \(E\) be a stable rank 2 vector bundle on a smooth quadric threefold \(Q\) in the projective 4-space \(P\) . We show that the hyperplanes \(H\) in \(P\) for which the restriction of \(E\) to the hyperplane section of \(Q\) by \(H\) is not stable form, in general, a closed subset of codimension at least 2 of the dual projective 4-space, and we explicitly describe the bundles \(E\) which do not enjoy this property. This refines a restriction theorem of Ein and Sols (Nagoya Math J 96:11–22, 1984) in the same way the main result of Coand? (J Reine Angew Math 428:97–110, 1992) refines the restriction theorem of Barth (Math Ann 226:125–150, 1977).