8 problems

Let an F-curve be an irreducible one-dimensional boundary stratum in the moduli space $\overline{\operatorname{M}}_{g,n}$, and let a type 6 F-curve denote an F-curve in the sixth c…

Let $M$ be a Fano manifold of Picard number one and let $\mathcal{E}$ be an ample vector bundle of rank $r$ on $M$. Let $L$, the extremal ray $R_1$, and a minimal rational curve…

Let $\overline{\operatorname{M}}_{g,n}$ be the moduli space of stable $n$-pointed curves, and let $F_5^{i,j}(I,\emptyset)$ denote a type 5 F-curve with parameters $i,j$ and marking…

Let $\overline{\operatorname{M}}_{g,n}$ be the moduli space of stable $n$-pointed curves of genus $g$, and let a boundary stratum mean an irreducible component of the locus of stab…

Let $(X,\Delta)$ be the dlt pair and setup of Theorem 1.6(iii), with a contraction morphism $iphi_{R_j}$ associated to a $(K_X+Delta)$-negative extremal ray $R_j$, and suppose…

Let $X$ be a complex $n$-dimensional Fano manifold with Picard number ${\rho}_X$. For every extremal ray $R$ of $X$, define its length by … Let $l_X$ be the minimum of $l(R)$ over…

ACC for lengths of extremal rays. For every $n$, the set $\mathcal L_n$ satisfies the ascending chain condition: if $X_k$ is an $n$-dimensional $\mathbb Q$-factorial log canonical…

Length-bound conjecture. The estimate $\leq 2\dim X$ should be replaced by $\leq \dim X+1$; that is, one should be able to choose $C$ with