Smooth projective toric varieties whose nontrivial nef line bundles are big

TL;DR

This paper constructs specific smooth projective toric varieties in any dimension greater than or equal to three, where all nontrivial nef line bundles are big, highlighting a particular geometric property.

Contribution

It provides explicit examples of high-dimensional toric varieties with the property that all nontrivial nef line bundles are big, for Picard number at least five.

Findings

Explicit construction of such toric varieties for all n ≥ 3

Demonstration that all nontrivial nef line bundles are big in these examples

Examples with Picard number ≥ 5

Abstract

For any $n\geq 3$, we explicitly construct smooth projective toric $n$-folds of Picard number $\geq 5$, where any nontrivial nef line bundles are big.