6 problems

Let $(X,B)$ be a klt pair, where $X$ is a normal $Q$-factorial compact Kähler variety. Let $\alpha\in H^{1,1}_{\rm BC}(X)$ be a nef class on $X$. If $\alpha-(K_X+B)$ is nef and big…

Base-point-freeness conjecture. The class $K_X + B + \alpha$ should be semiample: there should exist a holomorphic morphism $f:X\to Y$ onto a compact Kähler space and a Kähler clas…

Base-point-freeness conjecture. Under these hypotheses, the divisor $K_{\mathcal{F}}+B+A$ is semi-ample$/U$, and in the Cartier case its sufficiently high multiples are globally ge…

Base-point-freeness conjecture. For any integral $S_n$-invariant F-nef divisor $D$, $2D$ is $G$-base-point-free; in particular, $2D$ is base-point-free.

Karzhemanov's conjecture. Suppose that $X$ is $\mathbb{Q}$-factorial and

Reid's base point free conjecture. The linear system