A classification theorem on Fano bundles

TL;DR

This paper classifies rank two Fano bundles on certain Fano manifolds by analyzing their nef and pseudoeffective cones, revealing new insights into their structure and associated geometric properties.

Contribution

It provides a classification theorem for rank two Fano bundles on specific Fano manifolds using cone computations, a novel approach in this context.

Findings

Classification of rank two Fano bundles on specified Fano manifolds

Determination of cohomological invariants via cone analysis

Identification of multiple linear components in varieties of minimal rational tangents

Abstract

In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ${\mathbb{P}}(\cE)$, that allows us to obtain the cohomological invariants of $X$ and $\cE$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.