Rank two Weak Fano bundles on Fano threefolds of Picard rank one

TL;DR

This paper classifies rank two weak Fano bundles on Fano threefolds with Picard rank one, providing explicit examples and detailed resolutions, especially on the quadric threefold.

Contribution

It offers a comprehensive classification of rank two weak Fano bundles on Fano threefolds of Picard rank one, including explicit constructions and resolutions.

Findings

Complete classification of rank two weak Fano bundles

Existence of explicit examples for each classified case

Detailed resolutions on the quadric threefold

Abstract

We classify rank two vector bundles on a Fano threefold of Picard rank one whose projectivizations are weak Fano. We also prove the existence of examples for each case of the classification result. Our classification includes detailed resolutions of them on the quadric threefold.