A cohomological splitting criterion for rank 2 vector bundles on Hirzebruch surfaces

TL;DR

This paper provides a cohomological criterion to determine when rank 2 vector bundles on Hirzebruch surfaces split into simpler components, enhancing understanding of their structure.

Contribution

It introduces a new cohomological splitting criterion specifically for rank 2 vector bundles on Hirzebruch surfaces, filling a gap in existing classification methods.

Findings

Cohomological conditions for splitting are established.

All split rank 2 vector bundles on Hirzebruch surfaces are characterized.

The criterion simplifies the identification of split bundles.

Abstract

In this note, we give a cohomological characterization of all rank 2 split vector bundles on Hirzebruch surfaces.