The birational base change conjecture for discriminant divisors

Let $f:X\to Y$ be a contraction of normal varieties and let $K_X+B$ be a log divisor such that

• $K_X+B\sim_{\mathbb{Q},f}0$;
• $K_X+B$ is Kawamata log terminal over $\eta_Y$;
• $(X,B)$ has log nonsingular support and $\mathcal O_{Y,\eta_Y}=(f_*\mathcal O_X(\lceil-B\rceil))_{\eta_Y}$.

The Base Change Conjecture. Then $K_Y+B_Y$ is $\mathbb{Q}$-Cartier and, if $f':(X',B^{X'})\to Y'$ is induced by a birational base change $\sigma:Y'\to Y$, then

$$(B_Y)^{Y'}=(B^{X'})_{Y'},$$

so that

$$\sigma^*(K_Y+B_Y)=K_{Y'}+(B^{X'})_{Y'}.$$

The conjecture extends the finite-base-change theorem to birational base changes and predicts compatibility of the divisorial push-forward with such base changes. The source attributes it to work of Mori and Kawamata; the supplied text gives no resolution status.