Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs

Birkar, Caucher; Zhang, De-Qi

doi:10.1007/s10240-016-0080-x

Birkar, Caucher ¹ ; Zhang, De-Qi 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

Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 283-331.

Résumé

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.

MR Zbl

DOI : 10.1007/s10240-016-0080-x

Mots clés : Exceptional Divisor, Cartier Divisor, Kodaira Dimension, Picard Number, Generalize Adjunction

Affiliations des auteurs :

Birkar, Caucher ¹ ; Zhang, De-Qi ²

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     title = {Effectivity of {Iitaka} fibrations and pluricanonical systems of polarized pairs},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {283--331},
     publisher = {Springer Berlin Heidelberg},
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     volume = {123},
     year = {2016},
     doi = {10.1007/s10240-016-0080-x},
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Birkar, Caucher; Zhang, De-Qi. Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs. Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 283-331. doi : 10.1007/s10240-016-0080-x. http://www.numdam.org/articles/10.1007/s10240-016-0080-x/

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