Geodesic
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
Birkar, Caucher1  ; Zhang, De-Qi2
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 Cet article a éte moissonné depuis la source Numdam

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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.

DOI : 10.1007/s10240-016-0080-x
Keywords: 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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     title = {Effectivity of {Iitaka} fibrations and pluricanonical systems of polarized pairs},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {283--331},
     year = {2016},
     publisher = {Springer Berlin Heidelberg},
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     volume = {123},
     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

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