I will talk about a joint paper with Mihai Paun; our main result is that, for a fibration $p: X/rightarrow T$ from a projective manifold to a torus, the Kodaira dimension of $X$ is not less than the Kodaira dimension of the generic fiber. A main ingredient in our proof is a fine estimate about the weak positivity of the direct image of the relative pluri-canonical bundle.