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On the uniformity of the Iitaka fibration

On the uniformity of the Iitaka fibration

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 Iitaka(X) of smooth projective varieties of positive Kodaira dimension, provided that …