Jumping pairs of Steiner bundles
Enrique Arrondo, Simone Marchesi
TL;DR
This paper introduces Schwarzenberger bundles on Grassmannians, generalizes jumping pairs for Steiner bundles, and classifies those with maximal jumping locus dimension as Schwarzenberger bundles.
Contribution
It defines Schwarzenberger bundles on Grassmannians, extends the concept of jumping pairs for Steiner bundles, and classifies Steiner bundles with maximal jumping locus as Schwarzenberger bundles.
Findings
Classified Steiner bundles with maximal jumping locus as Schwarzenberger bundles.
Studied the jumping locus variety and established dimension bounds.
Provided a complete classification of these bundles.
Abstract
In this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus variety and bounding its dimension, we give a complete classification of Steiner bundle with jumping locus of maximal dimension, which all are Schwarzenberger bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra