Mathematical Research Letters

Volume 16 (2009)

Number 4

On the uniformity of the Iitaka fibration

Pages: 663 – 681

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n4.a9

Author

Gianluca Pacienza (Université de Strasbourg et CNRS)

Abstract

We study pluricanonical systems on smooth projective varieties of positive Kodaira dimension, following the approach of Hacon-McKernan, Takayama and Tsuji succesfully used in the case of varieties of general type. We prove a uniformity result for the Iitaka fibration $X\dra \Ii(X)$ of smooth projective varieties of positive Kodaira dimension, provided that $\Ii(X)$ is not uniruled, the variation of the fibration is maximal, and the general fiber has a good minimal model.

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