Semiample invertible sheaves with semipositive continuous hermitian metrics

Abstract

Let $\left(L,h\right)$ be a pair of a semiample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $ℂ$. In this paper, we prove that $\left(L,h\right)$ is semiample metrized, answering a generalization of a question of S. Zhang.