\] Assume the existence of good models for klt pairs in dimensions at most $n-0$. Let $X$ be a projective klt variety of dimension $n$ such that $K_X\sim_\Q0$, and let $\mathcal L$ be a nef line bundle on $X$.  0.  Assume that $\mathcal L$ has a singular hermitian metric with semipositive curvature current and with algebraic singularities. If $\chi(X,\OO_X)\neq0$, then $\kappa(X,\mathcal L)\geq0$.  0.  If $\mathcal L$ is hermitian semipositive and if $\chi(X,\OO_X)\neq0$, then $\mathcal L$ is semiample.  