Toric Fano manifolds with nef tangent bundles

TL;DR

This paper proves that all toric Fano manifolds with nef tangent bundles are products of projective spaces, confirming the Campana-Peternell conjecture for this class of manifolds.

Contribution

It establishes that such manifolds are necessarily products of projective spaces, providing a significant classification result.

Findings

Toric Fano manifolds with nef tangent bundles are products of projective spaces

Campana-Peternell conjecture holds for toric manifolds

Classification of these manifolds is now complete

Abstract

In this note we prove that any toric Fano manifold with nef tangent bundle is a product of projective spaces. In particular, it implies that Campana-Peternell conjecture hold for toric manifolds.