7 problems

Folklore conjecture. The normalized local volume carries no additional information at a non-closed point.

Let $(X\ni x,B)$ be an exceptionally non-canonical (enc) klt singularity, and let $\widehat{\operatorname{vol}}(X\ni x,B)$ denote its local volume. Positive lower-bound conjecture…

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…

Second-largest local volume conjecture. The second largest number in $\widehat{\rm Vol}_{n}$ is

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…

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…

Finite-degree multiplication conjecture. The local volumes satisfy