Let "X" be a variety of nonnegative Kodaira dimension over a field of characteristic zero, and let "B" be the canonical model of "X", "B" = Proj "R"("X", "K""X"); the dimension of "B" is equal to the Kodaira dimension of "X". There is a natural rational map "X" – → "B"; any morphism obtained from it by blowing up "X" and "B" is called the Iitaka fibration. The minimal model and abundance conjectures would imply that the general fiber of the Iitaka fibration can be arranged to be a Calabi–Yau variety, which in particular has Kodaira dimension zero. Moreover, there is an effective Q-divisor Δ on "B" (not unique) such that the pair ("B", Δ) is klt, "K""B" + Δ is ample, and the canonical ring of X is the same as the canonical ring of ("B", Δ) in degrees a multiple of some "d" > 0. In this sense, "X" is decomposed into a family of varieties of Kodaira dimension zero over a base ("B", Δ) of general type. (Note that the variety "B" by itself need not be of general type. For example, there are surfaces of Kodaira dimension 1 for which the Iitaka fibration is an elliptic fibration over P1.)