On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles

TL;DR

This paper investigates minimal singular Hermitian metrics on certain nef line bundles using Ueda theory, providing examples of nef bundles that lack smooth semi-positive curvature metrics.

Contribution

It introduces a method to identify minimal singular metrics on nef line bundles and demonstrates their properties with new examples.

Findings

Identification of minimal singular metrics for specific nef line bundles

Examples of nef line bundles without smooth semi-positive curvature metrics

Application of Ueda theory to singular Hermitian metrics

Abstract

We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$ whose local weights are plurisubharmonic. In some situations, we determine a minimal singular metric of $L$. As an application, we give new examples of (strictly) nef line bundles which admit no smooth Hermitian metric with semi-positive curvature.