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Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs

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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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Authors and Affiliations

  1. DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    Caucher Birkar

  2. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    De-Qi Zhang

Authors
  1. Caucher Birkar
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  2. De-Qi Zhang
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Correspondence to Caucher Birkar.

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Birkar, C., Zhang, DQ. Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Publ.math.IHES 123, 283–331 (2016). https://doi.org/10.1007/s10240-016-0080-x

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  • DOI: https://doi.org/10.1007/s10240-016-0080-x

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