Rank two Fano bundles on G(1,4)

TL;DR

This paper classifies rank two Fano bundles over the Grassmannian of lines G(1,4), showing that the universal quotient bundle is the only non-split example, thus completing the classification over Grassmannians of lines.

Contribution

It provides a complete classification of rank two Fano bundles over G(1,4), identifying the universal quotient bundle as the unique non-split case.

Findings

The only non-split rank two Fano bundle over G(1,4) is the universal quotient bundle, up to a twist.

The classification of rank two Fano bundles over Grassmannians of lines is now complete.

Abstract

We classify rank two Fano bundles over the Grassmannian of lines $\G(1,4)$. In particular we show that the only non-split rank two Fano bundle over $\G(1,4)$ is, up to a twist, the universal quotient bundle $\cQ$. This completes the classification of rank two Fano bundles over Grassmannians of lines.