Classification of Mukai pairs with corank $3$

TL;DR

This paper classifies Mukai pairs consisting of smooth Fano manifolds and ample vector bundles with specific rank and Chern class conditions, advancing understanding of their structure in algebraic geometry.

Contribution

It provides a complete classification of Mukai pairs with corank 3, detailing their structure for dimensions five and higher.

Findings

Classification of Mukai pairs with corank 3 completed

Identification of specific geometric structures of these pairs

Extension of known classifications in algebraic geometry

Abstract

We classify pairs $(X,\mathscr E)$ where $X$ is a smooth Fano manifold of dimension $n \geq 5$ and $\mathscr E$ is an ample vector bundle of rank $n-2$ on $X$ with $c_1(\mathscr E) = c_1(X)$.