4 problems

ACC conjecture for local volumes. If $b$ is finite, then the only accumulation point of $\operatorname{Vol}_{d,b}^{\operatorname{loc}}$ is $0$. If $b$ satisfies the descending chai…

Let $n$ be a positive integer, and let $\epsilon,\eta$ be positive numbers. A special degeneration of a klt singularity is the central fiber of a special test configuration as defi…

Let $n\geq 2$ be a positive integer and let $\eta,\epsilon$ be positive real numbers. Let $x\in (X,\Delta)$ be an $n$-dimensional klt singularity, with … where each…

Finite-degree multiplication conjecture. The local volumes satisfy