Fano n-folds with nef tangent bundle and Picard number greater than n-5

TL;DR

This paper proves that Fano n-folds with nef tangent bundle and high Picard number are necessarily rational homogeneous manifolds, advancing the classification of such algebraic varieties.

Contribution

It establishes a classification result for Fano n-folds with nef tangent bundle and Picard number exceeding n-5, showing they are all rational homogeneous.

Findings

Fano n-folds with nef tangent bundle and Picard number > n-5 are rational homogeneous.

Provides a classification criterion for these algebraic varieties.

Advances understanding of the structure of Fano manifolds with nef tangent bundles.

Abstract

We prove that Fano n-folds with nef tangent bundle and Picard number greater than n-5 are rational homogeneous manifolds.