EFFECTIVITY OF IITAKA FIBRATIONS AND PLURICANONICAL SYSTEMS OF POLARIZED PAIRS

For every smooth complex projective variety of dimension and nonnegative Kodaira dimension, we show the existence of a universal constant depending only on and two natural invariants of the very general fibres of an Iitaka fibration of such that the pluricanonical system defines an Iitaka fibration. This is a consequence of a more general result on polarized adjoint divisors. In order to prove these results we develop a generalized theory of pairs, singularities, log canonical thresholds, adjunction, etc.