The crepant smooth-resolution conjecture for abelian cspan class="math-inline"mathGammac/spancspan class="math-inline"mathsubseteq\operatorname{SU}$3$c/spancspan class="math-inline"math

Let $\Gamma\subset\operatorname{SU}(3)$ be an abelian group acting on $\mathbb{C}^3$ freely outside the origin. Let $X_0=\mathbb{C}^3/\Gamma$, and let $\rho_\zeta\colon X_\zeta\to X_0$ be the quotient morphism associated to a generic value of $\zeta$. Crepant smooth-resolution conjecture. The morphism $\rho_\zeta$ is crepant and $X_\zeta$ is smooth, so it is a smooth resolution of $X_0$. This is proposed as a good case in which the quotients $X_\zeta$ give natural, nonsingular minimal partial desingularisations; the source does not state a resolution of this conjecture.