3 problems

Let $(X,\Delta;x)$ be a klt singularity, and let $\operatorname{\widehat{vol}}(X,Delta;x)$ denote its normalized volume. Say that a collection of singularities is bounded up to spe…

Let $X$ be a toric singularity of dimension $d$, and suppose that its associated polytope $P$ is reflexive. Let $Y$ be the Gorenstein Fano variety corresponding to the face fan of…

Let $x\in (X,\Delta)$ be a klt singularity, and let … be its normalized volume function. A valuation $v^{\rm m}$ is a minimizer if it attains the infimum of this function. Chi Li's…