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# Positivity of direct image and Kodaira dimension

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Junyan Cao (Paris) - Seminar Algebraic Geometry (SAG)

What Seminar Oct 30, 2014 from 10:30 am to 11:30 am Bonn, Hörsaal MPI, Vivatsgasse 7 Sachinidis vCal iCal

Let $f: X\rightarrow Y$ be a fibration between two projective manifolds. The Iitaka's conjecture states that the Kodaira dimension of $X$ is larger than the sum of the Kodaira dimension of $X$ and the Kodaira dimension of the generic fiber. By using some deep results in mixed Hodge theory, Kollar proved that the Iitaka's conjecture is true if the generic fiber is of general type. By using some recent analytic methods, we give an alternative proof (without using Hodge theory ) of Kollar's result. We can also generalise it easily to the log canonical model case.