Inductive approach to effective b-semiampleness

It has been conjectured by Prokhorov and Shokurov that the moduli part in the canonical bundle formula is effectively b-semiample. In this work we reduce this conjecture to the case where the base of the fibration has dimension one. Moreover, in the case where the moduli part M is numerically trivial, we prove the existence of an integer m, that depends only on the middle Betti number of a canonical covering of the fibre, such that mM is linearly equivalent to the trivial bundle.