The Calabi–Yau ALE metric conjecture for $M_\zeta$

Let $M_\zeta$ be the ALE resolution constructed from the quotient $V/\Gamma$, and let $\omega_\zeta$ denote its Kähler form. The Calabi–Yau ALE metric conjecture. The ALE space $(M_\zeta,\omega_\zeta)$ is a Calabi–Yau ALE space of rate $-m$. The source presents this as a conjectural strengthening of the known ALE metric result, specifically in the dimensions $m=4$ and $m=6$; no general proof is supplied.