# Varieties fibered by good minimal models

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Ching-Jui Lai, University of Utah
Fine Hall 322

Let $f:X->Y$ be an algebraic fiber space such that the general fiber has a good minimal model. We show that if $f$ is the Iitaka fibration then $X$ has a good minimal model. The result reduces the minimal model conjecture to the case of varieties of Kodaira dimension zero and the non-vanishing conjecture.