Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 283-331.

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.

DOI : 10.1007/s10240-016-0080-x
Mots clés : Exceptional Divisor, Cartier Divisor, Kodaira Dimension, Picard Number, Generalize Adjunction
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
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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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