5 problems

Let $(X,B)$ be a projective lc pair. The divisor $K_X+B$ is assumed to be pseudo-effective, meaning that its numerical class lies in the closure of the cone generated by effective…

Let $(X,\Delta)$ be a projective klt pair of dimension $n$. Let $\operatorname{Nef}(X)$ be the nef cone, let $\operatorname{Sem}(X)$ be the cone of semiample divisors, and let…

Let $(X,\Delta)$ be a log pair, with $X$ normal and $\Delta$ an effective formal $\mathbb{Q}$-linear combination of prime divisors. The pair is log canonical if all discrepancies a…

Log abundance conjecture. If $K_X+B$ is nef, then it is semi-ample.

Prokhorov–Shokurov conjectures. The following properties are conjectured: