Varieties fibered by good minimal models

Abstract

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 or if f is the Albanese map of relative dimension no more than three, then X has a good minimal model.Comment: 12 pages. Correction of definition of vertical part of a divisor. A more precise (well-known) description of V_m(K_X) has been adde