arXiv 0807.16452008-07math.AG

Schwarzenberger bundles of arbitary rank on the projective space

Enrique Arrondo

备注：: 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

英文摘要：

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 ${\Bbb P^n}$ (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.

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