Semiample invertible sheaves with semipositive continuous hermitian metrics

TL;DR

This paper proves that semiample invertible sheaves with semipositive continuous hermitian metrics are semiample metrized, extending previous questions posed by S. Zhang in the context of algebraic geometry.

Contribution

The paper generalizes the concept of semiample metrization to a broader class of sheaves with continuous hermitian metrics, building on prior work by S. Zhang.

Findings

Established semiample metrization for semiample invertible sheaves with semipositive continuous hermitian metrics.

Extended the understanding of metric properties of line bundles in algebraic geometry.

Provided a positive answer to a question posed by S. Zhang.

Abstract

Let (L, h) be a pair of a semiample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety. In this paper, we prove that (L, h) is semiample metrized, which is a generalization of the question due to S. Zhang.