4 problems

Numerical semi-ampleness conjecture. Every nef line bundle $L$ on $X$ is numerically semi-ample; that is, there exists a semi-ample line bundle $L'$ on $X$ such that

Abundance conjecture. If the restriction $[mD]|_Y$ is holomorphically trivial for some positive integer $m$, then the complete linear system $|mD|$ should yield a fibration on $X$;…

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 $(X/Z,B)$ 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-…