3 problems

Hyperkähler cone conjecture. Any conical symplectic singularity is a hyperkähler cone.

Fano-cone Ricci-flatness conjecture. On a Fano cone $X$, every Kähler-Ricci shrinker is a Ricci-flat Kähler cone metric.

Let $n$ be a positive integer. A set of klt singularities is bounded if all its members occur as fibers of one $\mathbb{Q}$-Gorenstein family; for Fano cone singularities, the fami…