Remarks on toric manifolds whose Chern characters are positive

TL;DR

This paper investigates the positivity properties of Chern characters in projective toric manifolds, proving the non-ampleness of the second Chern character in certain cases and providing examples of positive higher Chern characters.

Contribution

It establishes a non-ampleness result for the second Chern character in Picard number three toric manifolds and presents examples of positive higher Chern characters.

Findings

Second Chern character is not ample for Picard number three toric manifolds.

Examples of positive higher Chern characters in projective toric manifolds.

Insights into the positivity properties of Chern characters in toric geometry.

Abstract

We show that the second Chern character of any projective toric manifold of Picard number three is not ample. In connection with this result, we give various examples of the positivity of higher Chern characters of projective toric manifolds.