Semiample invertible sheaves with semipositive continuous hermitian   metrics
  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. 
Atsushi Moriwaki
math.AG math.NT