6 problems

Let $X$ be a normal $3$-dimensional variety and let $Delta_X$ be an effective ${\Bbb Q}$-divisor such that $(X,\Delta_X)$ is Kawamata log terminal. Let … be a log $(K_X+\Delta_X)$-…

Let … be a sequence of flips over $Z$, starting from a log canonical pair $(X_1,B_1)$ of dimension $d$. Let $\operatorname{LCS}(X_i,B_i)$ denote the locus of log canonical singular…

Let $(Y',B_{Y'})$ be a pair, and let $\mathfrak{M}(Y',B_{Y'})$ denote the set of b-free b-divisors that are log canonically saturated, meaning … A model has canonically confined si…

Let $(Y/T,B)$ be a weak log Fano contraction, in particular Klt, and let $\{\mathcal{D}_i\}_{i=1}^{\infty}$ be a system of b-divisors. Assume that $\{\mathcal{D}_i\}$ satisfies the…

Ambro–Shokurov's lower semicontinuity conjecture. For each $d$, the function

Ambro–Shokurov's ACC conjecture. The set $\Omega_k$ is an ACC-set: every increasing sequence $\alpha_1\leq\alpha_2\leq\cdots$ in $\Omega_k$ eventually becomes stationary.