Basepoint-free theorems: Saturation, b-divisors, and canonical bundle formula

Abstract

We reformulate basepoint-free theorems using notions introduced by Shokurov, such as b-divisors and saturation of linear systems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the basepoint-free theorem in Fukuda's paper "On numerically effective log canonical divisors". © 2012 by Mathematical Sciences Publishers.