3 problems

Let $G_K\cong \mathrm{PSL}_2(\mathbb{F}_7)$ be the Klein simple group, and let $X_n/\mathbb{P}^1$ be the $G_K$-Mori fiber spaces described above. A $G_K$-Mori fiber space is a thre…

Weak BAB conjecture for Mori fiber spaces. Fix $0<\epsilon<1$ and an integer $n>0$. Then there exists a number $M(n,\epsilon)$ depending only on $n$ and $\epsilon$ such that, if…

McKernan's conjecture. There exists a number $\delta=\delta_{m,n}(\epsilon)>0$ such that, whenever $X$ is a $\mathbb Q$-factorial variety, $f\colon X\to Y$ is a Mori fiber space wi…