Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent bundle). We show that the Hilbert scheme of m points of these surfaces is again a moduli space of parabolic Higgs bundles (respectively, local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky-Nekrasov-Rubtsov. Using the McKay correspondence, we establish the autoduality conjecture for the derived categories of the moduli spaces of Higgs bundles under consideration.
Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia