Jumping spaces in Steiner Bundles

In this work we will study Steiner and Schwarzenberger bundles on the grassmannians. In the first part we will define Steiner bundles on G(k,n), agreeing with the definition proposed by Miró-Roig and Soares for any projective variety. We will define then the concept of Schwarzenberger bundle for any rank on the grassmannian, which represents the generalization of the definition proposed by Arrondo. We will introduce the concept of jumping pair for a Steiner bundle and we will investigate the dimension of the jumping locus of the bundle. Finally, we will give a complete classification of Steiner bundles on the grassmannian whose jumping locus has maximal dimension and we will describe them as Schwarzenberger bundles.