Extension of the Hitchin–Calabi–Yau correspondence to general singular elliptic Calabi–Yau threefolds

Let a compact singular elliptically fibered Calabi–Yau $3$-fold have singular fibers associated to ${\mathcal G}$-symmetry in codimension $1$ over the base, admit a crepant resolution, and let an ${\mathcal H}$-type Hitchin system be defined over the discriminant locus of the elliptic fibration, with ${\mathcal H}\subset { \mathcal G}$. Hitchin–Calabi–Yau correspondence conjecture. The correspondence between the Hitchin system on the discriminant locus and the local part of the compact Calabi–Yau integrable system extends to these geometries. The source presents this as a proposed extension of a correspondence established for singular Calabi–Yau threefolds with $A_n$-type singularities.