Hilbert schemes as moduli of Higgs bundles and local systems

Michael Groechenig

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arXiv · 1206.5516

Hilbert schemes as moduli of Higgs bundles and local systems

Michael Groechenig

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Abstract

We construct five families of two-dimensional 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. 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.

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BibTeX RIS

Michael Groechenig. 2012-06-24. Hilbert schemes as moduli of Higgs bundles and local systems. https://arxiv.org/abs/1206.5516

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