The determinant equality conjecture for Kodaira dimensions of fibrations

Let $f\colon X \to Y$ be a fibration between smooth projective varieties with general fiber $F$ and $\kappa(Y)\ge0$. For a sufficiently divisible positive integer $m$ such that $f_*\omega_X^{\otimes m}\ne0$, consider the determinant line bundle $\widehat{\det} f_*\omega_X^{\otimes m}\otimes\omega_Y$. The determinant equality conjecture.

$$\kappa(X)=\kappa(F)+\kappa\bigl(Y,\widehat{\det} f_*\omega_X^{\otimes m}\otimes\omega_Y\bigr).$$

The conjecture predicts an equality refining known superadditivity statements for Kodaira dimension. The paper introduces it as a proposed conjecture; its general status is open.