11 problems

Let $a\geq0$ and $d$ be a nonnegative integer. The sets $\mathcal S_d\text{(global)}$, $\mathcal S_d^0\text{(global)}$, $\mathcal S_{a,d}\text{(local)}$,…

McKernan's ACC conjecture. There exists an ACC set $\Gamma\subset [0,1]$ depending only on $d$ such that, for every such $\mathcal{F}$ on $X$, the threshold…

Let $n$ be a positive integer. ACC conjecture. The set of all possible local volumes $\widehat{\rm vol}(x,X)$ of $n$-dimensional klt singularities is discrete away from zero. This…

Let $n$ be a fixed positive integer. The local volume $\widehat{\rm vol}(x,X)$ is the normalized-volume invariant of an $n$-dimensional klt singularity $x\in X$. ACC conjecture for…

ACC conjecture for foliated minimal log discrepancies. For every positive integer $d$, the set

Let $d\in\mathbb{Z}_{>0}$ and let $I\subset[0,+\infty)$ be a subset satisfying the DCC. Define … where $M\in I$ has the meaning specified in the source's definition of generalized…

ACC conjecture for local volumes. (1) If $I$ is finite, then $\operatorname{Vol}^{\operatorname{loc}}_{n,I}$ has $0$ as its only accumulation point. (2) If $I$ satisfies the DCC, t…

Let $P(X/Z\ni z,\Delta;D_1,\ldots,D_s)$ denote the set of vectors $(t_1,\ldots,t_s)\in\mathbb{R}_{\ge0}^s$ for which $(X/Z\ni z,\Delta+t_1D_1+\cdots+t_sD_s)$ is…

Let $P\in(X,\mathfrak{a})$ be a germ of a pair on a nonsingular variety $X$ of dimension $d$, where $\mathfrak{a}$ is an $\mathbb{R}$-ideal, and let…

ACC conjecture for log canonical thresholds. The set

Global ACC conjecture. There is a finite subset $I_0\subset I$ such that, whenever $X$ is a projective variety of dimension $d$, $(X,\Delta)$ is log canonical, each $\delta_i\in I$…