Toric varieties with ample tangent bundle

TL;DR

This paper provides a straightforward combinatorial proof of a classification theorem stating that the only smooth projective toric varieties with an ample tangent bundle are projective spaces.

Contribution

It offers a simple combinatorial proof of the toric Mori's theorem, confirming the uniqueness of projective spaces among such varieties.

Findings

Only projective spaces have ample tangent bundles among smooth projective toric varieties.

The proof simplifies previous arguments using combinatorial methods.

Supports the classification of varieties with positive tangent bundle properties.

Abstract

We give a simple combinatorial proof of the toric version of Mori's theorem that the only $n$-dimensional smooth projective varieties with ample tangent bundle are the projective spaces $\mathbb{P}^n$.