Numerical semiampleness of nef adjoint classes on compact Kähler manifolds

Abstract — v1

Let $X$ be a smooth connected compact Kähler manifold, let $B$ be an effective rational simple normal crossing divisor with coefficients less than one, and let $M$ be a nef rational holomorphic line bundle on $X$. If $K_X+B$ is pseudo-effective and $K_X+B+M$ is nef, we prove that its first Chern class in real Bott–Chern cohomology is represented by a semiample rational line bundle. This numerical statement allows a flat change of line bundle; it does not assert semiampleness of the original adjoint.