We study how the Aharonov–Bohm effect is reflected in the location of quantum resonances for scattering by three solenoids at large separation. We also discuss what happens in the case of four solenoids.

We extend the framework of K-stability~[30],~[8] to a more general algebro-geometric setting, such as partial desingularisations of fixed singularities, (not necessarily flat) families over higher dimensional base and birational geometry of surfaces.

We also observe that “concavity” of the volume function implies decrease of the (generalised) Donaldson–Futaki invariants along the Minimal Model Program, in our generalised settings. Several related results on the connection with the MMP theory, some of which are new even in the original setting of families over curves, are also proved.