Uniform vector bundles on Fano manifolds and applications

TL;DR

This paper establishes a criterion for splitting uniform vector bundles on Fano manifolds covered by lines, leading to classifications of low rank bundles on Hermitian symmetric spaces and rank two Fano bundles on Grassmannians.

Contribution

It introduces a new splitting criterion for uniform vector bundles on Fano manifolds and classifies specific low rank bundles on symmetric spaces and Grassmannians.

Findings

Splitting criterion for uniform vector bundles on Fano manifolds.

Classification of low rank uniform vector bundles on Hermitian symmetric spaces.

Classification of rank two Fano bundles on Grassmannians.

Abstract

In this paper we give a splitting criterion for uniform vector bundles on Fano manifolds covered by lines. As a consequence, we classify low rank uniform vector bundles on Hermitian symmetric spaces and Fano bundles of rank two on Grassmannians.