Schwarzenberger bundles on smooth projective varieties

TL;DR

This paper introduces Schwarzenberger bundles on smooth projective varieties, studies their jumping pairs, and classifies Steiner bundles with maximal jumping loci as Schwarzenberger bundles.

Contribution

It defines Schwarzenberger bundles on arbitrary smooth projective varieties and classifies Steiner bundles with maximal jumping loci as Schwarzenberger bundles.

Findings

Bound for the dimension of the jumping locus of Steiner bundles.

Complete classification of Steiner bundles with maximal jumping pairs.

Identification of these bundles as Schwarzenberger bundles.

Abstract

We define Schwarzenberger bundles on any smooth projective variety X. We introduce the notions of jumping pairs of a Steiner bundle E on X and determine a bound for the dimension of its jumping locus. We completely classify Steiner bundles whose set of jumping pairs have maximal dimension, proving that they are all Schwarzenberger bundles.