6 problems

Log abundance conjecture. The linear system $|m(K_X+\Delta)|$ is base point free for some $m\in\mathbb{N}$.

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…

Prokhorov–Shokurov conjectures. The following properties are conjectured:

Log abundance conjecture. $K_X+\Delta$ is semi-ample.