On the classification of rank 2 almost Fano bundles on projective space

TL;DR

This paper investigates rank 2 almost Fano bundles on projective spaces, establishing their existence only on almost Fano manifolds and providing a classification framework for these bundles.

Contribution

It proves that rank 2 almost Fano bundles on projective spaces exist exclusively on almost Fano manifolds and offers insights into their structure.

Findings

Almost Fano bundles only exist on almost Fano manifolds

Classification results for rank 2 almost Fano bundles on projective spaces

New criteria for the existence of such bundles

Abstract

An almost Fano bundle is a vector bundle on a smooth projective variety that its projectivization is an almost Fano variety. In this paper, we prove that almost Fano bundles exist only on almost Fano manifolds and study rank 2 almost Fano bundles over projective spaces.