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arXiv · 1410.0938

Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs

Caucher Birkar·De-Qi Zhang
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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 $|mK_W|$ 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.

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Caucher Birkar, De-Qi Zhang. 2014-10-03. Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. https://arxiv.org/abs/1410.0938

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