Iitaka–Viehweg conjecture for algebraic fiber spaces

Let $f\colon X\to Y$ be an algebraic fiber space between smooth projective varieties, with general fiber $F$. Assume that $\kappa(Y)\geq 0$, and let $\operatorname{var}(f)$ denote the birational variation in the moduli of the fibers.

Iitaka–Viehweg conjecture. The Kodaira dimension of $X$ satisfies

$$\kappa(X)\geq \kappa(F)+\max\{\kappa(Y),\operatorname{var}(f)\}.$$

This refines the expected subadditivity of Kodaira dimension in algebraic families by incorporating the birational variation of the fibers. The supplied source context identifies the surrounding result as a special case of Iitaka's $C_{n,m}$ conjecture, but does not state whether this precise formulation has been resolved.