# Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

## TL;DR

This paper classifies complex Fano manifolds containing a special negative divisor isomorphic to a rational homogeneous space with Picard number one, extending previous research in algebraic geometry.

## Contribution

It provides a complete classification of pairs (X, A) where X is a Fano manifold and A is a rational homogeneous divisor with an ample conormal bundle.

## Key findings

- Complete classification of pairs (X, A) under given conditions.
- Extension of previous classification results by Tsukioka, Watanabe, Casagrande-Druel.
- Identification of new geometric structures in Fano manifolds.

## Abstract

Let $X$ be an $n$-dimensional complex Fano manifolds $(n\geq 3)$. Assume that $X$ contains a divisor $A$, which is isomorphic to a rational homogeneous space with Picard number one, such that the conormal bundle $\mathscr{N}^*_{A/X}$ is ample over $A$. Building on the works of Tsukioka, Watanabe and Casagrande-Druel, we give a complete classification of such pairs $(X,A)$.