  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.
