The self-duality conjecture for Ricci-flat orbifold limits bubbling Eguchi–Hanson metrics

Let $(M_n,\mathbf{g}_n)_n$ be a sequence of compact smooth Ricci-flat metrics converging in the Gromov–Hausdorff sense to a Ricci-flat orbifold $(M_o,\mathbf{g}_o)$, while Eguchi–Hanson metrics bubble at the singularities. Self-duality conjecture. The curvature of $\mathbf{g}_o$ at its singular points is either selfdual or anti-selfdual, according to the orientation of the Eguchi–Hanson metrics. The statement is motivated by higher-order obstruction calculations and already holds under a stability assumption according to the surrounding text; the unrestricted claim is presented as conjectural.