Symplectic geometry of Higgs moduli and the Hilbert scheme of points over an elliptic curve

Abstract

We show that the isomorphism between the moduli space of certain parabolic Higgs bundles over an elliptic curve and the Hilbert scheme of n points of the cotangent bundle of the elliptic curve is a symplectomorphism with respect to their natural symplectic structures.

11 pages, all results of this paper are subsumed by arXiv:2608.12093