"Pluricanonical systems on algebraic varieties of positive Kodaira dimension" Gianluca PACIENZA (Univ. Strasbourg)
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 arbitrary (positive) Kodaira dimension such that Iitaka(X) is not uniruled. For certain classes of varieties (e.g. for 3-folds) this extra condition can be dropped.
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