| 概要 | Let  be an algebraic fiber space with generic geometric fiber
 ,  and  . Then Iitaka's  conjecture states
\geq \kappa (Y)+\kappa (F).)
In particular, if  is a
variety with =0) and  is the Albanese map, then Ueno
conjecture that =0) . One can regard Ueno's conjecture an
important test case of Iitaka's conjecture in general.
These conjectures are of fundamental importance in the classification of
higher dimensional complex projective varieties. In a recent joint work
with Hacon, we are able to prove Ueno's conjecture and conjecture
holds when  is of maximal Albanese dimension. In this talk, we will
introduce some relative results and briefly sketch the proof.
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