The global moduli fibration conjecture for special-holonomy QALE resolutions

Let $V$ be a vector space, let $\Gamma\subset\operatorname{SU}(V)$ be finite, and assume that $V/\Gamma$ admits a crepant resolution. Let $\Theta_{\operatorname{Im}(\mathbb{K})}$ denote the relevant parameter space. The global moduli fibration conjecture. There exists a stratified Riemannian fibration

$$\kappa:\mathbb{M}\to\Theta_{\operatorname{Im}(\mathbb{K})}$$

equivariant under $\mathbb{R}_{>0}\times N_{\operatorname{SO}(V)}(\Gamma)$, equipped with an Ehresmann connection $\check{H}$ and a vertically closed differential form of the stated Calabi–Yau or hyperkähler type. Its fibres are special-holonomy QALE spaces resolving $V/\Gamma$ and fit together in a family via the displayed maps $\rho_\zeta$. This conjectures a global parameter-space geometry extending the known local quotient constructions; the source gives no resolution.