Schwarzenberger bundles on smooth projective varieties

We define Schwarzenberger bundles on smooth projective varieties and we introduce the notions of jumping subspaces and jumping pairs of (F0,OX)(F0,OX)-Steiner bundles. We determine a bound for the dimension of the set of jumping pairs. We classify those Steiner bundles whose set of jumping pairs has maximal dimension by proving that they are Schwarzenberger bundles.