2 problems

Let $G$ be any finite subgroup of $\operatorname{SL}(3,\mathbb{C})$, and let $\mathcal{H}^G(\mathbb{C}^3)$ denote the $G$-Hilbert scheme. Nakamura's conjecture. The space…

Let $G$ be a finite abelian subgroup of ${\operatorname{GL}}(n,\Bbbk)$, and let ${G}\operatorname{-Hilb}$ denote the associated $G$-Hilbert scheme. Disconnectedness conjecture. The…