4 problems

Let $Y$ be a compact complex manifold of dimension $n+1$, let $F$ be a holomorphic line bundle on $Y$, and for a smooth closed $(1,1)$-form $\alpha$ define … Here the infimum is ov…

Let $Y$ be a compact complex manifold of dimension $n$, let $F$ be a holomorphic line bundle on $Y$, and define … For a smooth closed $(1,1)$-form $\alpha$ in $c_1(F)$, let…

Cao–Tsuji conjecture. The limit

Asymptotic purity conjecture. $X$ is AP if and only if the big and ample cones are equal.