Schwarzenberger bundles of arbitary rank on the projective space
Algebraic Geometry
2008-10-10 v3
Abstract
We 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 (which in rank coincides with the notion of unstable hyperplane introduced by Vall\`es, 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.
Keywords
Cite
@article{arxiv.0807.1645,
title = {Schwarzenberger bundles of arbitary rank on the projective space},
author = {Enrique Arrondo},
journal= {arXiv preprint arXiv:0807.1645},
year = {2008}
}
Comments
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 LaTeX