For minimal surfaces admitting an elliptic fibration over a smooth curve, there is a famous analysis of possible singular fibers and a canonical bundle formula due to Kodaira.
There are two papers of Kenji Ueno, in which he tries to classify the singular fibers of an abelian surface fibration over a smooth curve. But I don't see any formula for the canonical bundle of such threefolds?
Does any body know of any formula for that?
(All the varieties I am talking about are projective)