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2009•Mathematical Research LettersOpen access

On the uniformity of the Iitaka fibration

Gianluca Pacienza

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

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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 Iitaka(X) is not uniruled, the variation of the fibration is maximal, and the general fiber has a good minimal model.

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Available 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 Iitaka(X) of smooth projective varieties of positive Kodaira dimension, provided that Iitaka(X) is not uniruled, the variation of the fibration is maximal, and the general fiber has a good minimal model.

Key concepts: Fibration, Kodaira dimension, Mathematics, Dimension (graph theory), Pure mathematics, Fiber, Projective test, Type (biology)

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