5 problems

Let $(X,\Delta)$ be a klt log Calabi–Yau pair, meaning that $X$ is smooth projective and $\Delta \in |-K_X|$ is linearly equivalent to $\sum_i a_iD_i$ for effective divisors $D_i$…

Let $Y$ be a Calabi–Yau manifold, and let $\overline{\mathrm{Mov}}^+(Y)$ denote the rational hull of its closed movable cone. A pseudo-automorphism of $Y$ is a small modification…

Let $(X,\Delta)$ be a projective klt pair of dimension $n$, and fix an integer $k$ with $0\leq k\leq n-1$. Let $\operatorname{Mov}^k(X)$ be the cone generated by numerical classes…

Let $X$ be a Calabi–Yau variety, and consider its movable cone and the minimal models birational to $X$. Movable-cone Cone Conjecture. The variety $X$ should have only finitely man…

Let $Z$ be a smooth Fano manifold of dimension at least $4$, and assume that the linear system $|{-}K_Z|$ is free. Movable cone conjecture for general anticanonical hypersurfaces.…