7 problems

Let $(X,\Delta) \to S$ be a klt Calabi–Yau fiber space. Let $\Gamma_B$ and $\Gamma_A$ be the images of the pseudo-automorphism group $\operatorname{PsAut}(X/S,\Delta)$ and the auto…

Polyhedral-covering conjecture.

Standard minimal model program conjecture. The standard conjecture of the minimal model program predicts that a variety with intermediate Kodaira dimension birationally admits a Ca…

Finiteness conjecture. The group $\Gamma_W$ is always finite. The preceding lemma proves finiteness under the stronger assumption that $X$ has terminal singularities; the conjectur…

Let $f:(X,\Delta)\to S$ be a klt Calabi–Yau fiber space. Let $\operatorname{Eff}(X/S)$, $\operatorname{Mov}(X/S)$, and $\operatorname{Amp}(X/S)$ denote the effective, movable, and…

Let $X$ be a projective Calabi–Yau $4$-fold admitting a Calabi–Yau $3$-fold fibration … over a smooth curve $C$. Let $X_p=\pi^{-1}(p)$ be a general fiber and let…

Uniform diameter bound. There is a constant $C$ such that, independently of $t$ and the fibre $X_y$,