The ODP conjecture on normalized volumes of klt singularities

Let $(\mathcal{V}_p,p)$ be a non-smooth $n$-dimensional klt singularity, and let $\hat{vol}(\mathcal{V}_p)$ denote its normalized volume. An ordinary double point is the singularity defined by

$$\sum_i z_i^2=0.$$

ODP conjecture.

$$\hat{vol}(\mathcal{V}_p)\leq 2(n-1)^n,$$

with equality holding precisely for the ordinary double point singularity.

This conjecture proposes a gap between the normalized volume of a non-smooth klt singularity and the smooth value $\hat{vol}(\mathbb{C}^n)=n^n$. It is attributed in the source to Spotti and Liu; its resolution status is not specified here.