The additivity conjecture for smooth projective families over quasi-projective bases

Let $f\colon U\to V$ be a smooth projective algebraic fiber space between smooth quasi-projective varieties, and let $F$ be its general fiber. The quasi-projective additivity conjecture. One should have

$$\kappa(U)=\kappa(F)+\kappa(V).$$

This is the strongest proposal in the note and is stated to imply the preceding conjectures. It is known in several important cases, including when the base is of log general type, when the base is a curve, and when the general fiber has a good minimal model; the general statement remains open.