From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes
By establishing the smoothness, connectedness, and Poisson structure of orbifold Hilbert schemes on projective orbifold surfaces, this paper constructs natural compactifications of two-dimensional Hitchin systems associated with affine Dynkin diagrams , and as rational elliptic surfaces with -actions that arise from iterated blow-ups of the second Hirzebruch surface.