Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs

Abstract

For every smooth complex projective variety $W$ of dimension $d$ and nonnegative Kodaira dimension, we show the existence of a universal constant $m$ depending only on $d$ and two natural invariants of the very general fibres of an Iitaka fibration of $W$ such that the pluricanonical system $|m{K}_W|$ 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.

46 pages, final version to appear in Pub. Math. IHES

References in corpus (2)

• On existence of log minimal models
• Boundedness of log Calabi-Yau pairs of Fano type

Cited by in corpus (2)

• Some Results about the Index Conjecture for log Calabi-Yau Pairs
• Boundedness of log Calabi-Yau pairs of Fano type