4 problems

Variant of Shokurov's b-semi-ampleness conjecture. For all $m\gg 0$ and any $\epsilon\in\mathbb Q_{>0}$, the divisor

Let $f\colon (X, B_X) \to (Y,D)$ be a very basic slc-trivial fibration, where $D$ is the divisor in its structure decomposition. The abundance conjecture. If $D$ is nef, then $D$ i…

Let $f:(X, B)\to Y$ be a basic slc-trivial fibration, and let $\mathbf M$ denote its moduli part, a moduli $\mathbb Q$-b-divisor on $Y$. B-semi-ampleness conjecture. The moduli par…

Let $(X/Z,B)$ be a $\mathbb Q$-factorial dlt pair, and let … Assume that $B$ is a $\mathbb Q$-divisor and $Z$ is affine. Suppose that $K_X+B$ is nef$/Z$, that $(K_X+B)|_S$ is semi-…