2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171063We introduce a generalized notion of Schwarzenberger bundle on the projective space. Associated to this more general definition, we give an ad-hoc notion of jumping subspaces of a Steiner bundle on ${\Bbb P^n}$ (which in rank $n$ coincides with the notion of unstable hyperplane introduced by Vallès, Ancona and Ottaviani). For the set of jumping hyperplanes, we find a sharp bound for its dimension. We also classify those Steiner bundles whose set of jumping hyperplanes have maximal dimension and prove that they are generalized Schwarzenberger bundles.v3 is the submitted version of the paper. It differs from v2 in the correction of some typos, the reconstruction of the proof of Lemma 3.6, and that now it is re-written in LaTeXAlgebraic Geometry14F05; 14N05text