Semiampleness for generalized pairs

Abstract

We prove that if $(X,B+\mathbf{M})$ is a generalized klt pair with $K_X+B+{\mathbf{M}}_X$ nef and abundant, then $K_X+B+{\mathbf{M}}_X$ is semiample. More generally, we prove a generalized basepoint free theorem for generalized klt pairs.

New corollary added to the previous version. No other changes. Comments welcome