Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

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.


Published in:
International Mathematics Research Notices, 23, 6523-6575
Year:
2014
Publisher:
Oxford, Oxford Univ Press
ISSN:
1073-7928
Laboratories:




 Record created 2015-02-20, last modified 2018-03-17


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