The Cautis-Logvinenko conjecture
For a finite subgroup $G\subset \operatorname{SL}(3,\mathbb{C})$, the Cautis--Logvinenko conjecture states that for each nontrivial irreducible representation $\rho$ of $G$, the image of the sheaf $\mathcal{O}_0\otimes \rho$ under the derived equivalence of Bridgeland--King--Reid is a pure sheaf on the $G$-Hilbert sche...