4 problems

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 $(X,\Delta)$ 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…