On the uniformity of the Iitaka fibration

Details On the uniformity of the Iitaka fibration On the uniformity of the Iitaka fibration

2007-09-03

arxiv.org/abs/0709.0310v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

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 of smooth projective varieties of positive Kodaira dimension, provided that the base of the Iitaka fibration is not uniruled, the variation of the fibration is maximal, and the generic fiber has a good minimal model.

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