# Nestings of rational homogeneous varieties

## TL;DR

This paper investigates the existence of special sections called nestings on rational homogeneous varieties, providing a complete classification for varieties with automorphism groups of classical simple Lie algebra type.

## Contribution

It offers a complete classification of nestings on rational homogeneous varieties with simple classical automorphism groups, establishing conditions for their existence.

## Key findings

- Nestings do not exist unless a proper algebraic subgroup acts transitively.
- Complete classification of nestings for varieties with classical simple automorphism groups.
- Identifies conditions under which nestings can occur.

## Abstract

In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is simple of classical type. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety.