Gromov-Hausdorff convergence of non-collapsed polarized cscK surfaces is realized as Hilbert scheme convergence, with Bergman kernel estimates enabling Zariski openness of cscK metrics in smooth polarized families.
Singular cscK metrics on smoothable varieties
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On the geometry of non-collapsed polarized cscK surfaces
Gromov-Hausdorff convergence of non-collapsed polarized cscK surfaces is realized as Hilbert scheme convergence, with Bergman kernel estimates enabling Zariski openness of cscK metrics in smooth polarized families.