Weak Fano bundles of rank $2$ over hyperquadrics $Q^n$ of dimension $n \ge 5$

TL;DR

This paper classifies rank 2 weak Fano bundles over high-dimensional quadrics $Q^n$ for $n \,\ge 5$, expanding understanding of vector bundles with weak Fano projectivizations in algebraic geometry.

Contribution

It provides the first classification results for rank 2 weak Fano bundles on quadrics of dimension five and higher.

Findings

Classification of rank 2 weak Fano bundles on $Q^n$ for $n \ge 5$

Identification of conditions under which the projectivization is a weak Fano variety

Extension of known results to higher-dimensional quadrics

Abstract

A vector bundle whose projectivization becomes a weak Fano variety is called a weak Fano bundle. We present classification results for rank 2 weak Fano bundles on higher-dimensional quadrics $Q^n$ of dimension $\ge 5$.