PUBLICATIONS MATHÉMATIQUES DE L'IHES

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Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
Caucher Birkar1 ; De-Qi Zhang2
1 DPMMS, Centre for Mathematical Sciences, University of Cambridge Wilberforce Road CB3 0WB Cambridge UK
2 Department of Mathematics, National University of Singapore 10 Lower Kent Ridge Road 119076 Singapore Singapore
Publications Mathématiques de l'IHÉS, Volume 123 (2016), pp. 283-331
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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 |mKW| 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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DOI: 10.1007/s10240-016-0080-x
Keywords: Exceptional Divisor, Cartier Divisor, Kodaira Dimension, Picard Number, Generalize Adjunction

Caucher Birkar 1; De-Qi Zhang 2

1 DPMMS, Centre for Mathematical Sciences, University of Cambridge Wilberforce Road CB3 0WB Cambridge UK
2 Department of Mathematics, National University of Singapore 10 Lower Kent Ridge Road 119076 Singapore Singapore 
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Caucher Birkar; De-Qi Zhang. Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Publications Mathématiques de l'IHÉS, Volume 123 (2016), pp. 283-331. doi: 10.1007/s10240-016-0080-x

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