On the pluricanonical maps of varieties of intermediate Kodaira dimension

In this paper we will prove a uniformity result for the Iitaka fibration $f:X\rightarrow Y$ , provided that the generic fiber has a good minimal model and the Prokhorov–Shokurov conjecture holds. In particular, the result holds if the variation of $f$ is zero or $\kappa (X)=\text{ dim}X-1$ .