2 problems

Let $(X,B)$ be a log variety, let $x\in X\setminus LCS(X,B)$ be a closed point, and let $H\in\operatorname{Div}(X)\otimes\mathbb{Q}$ be ample and normalized at $x$. Effective-build…

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