A stability-preserving map T from star-shaped Nakajima quiver varieties to central-Levi parabolic Higgs bundle moduli spaces is a homeomorphism on the trivial holomorphic structure locus and identifies their holomorphic symplectic structures.
Wild nonabelian Hodge theory on curves
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abstract
On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are obtained by fixing at each singularity the polar part of the connection. We prove that they carry hyperKahler metrics, which are complete when the residue of the connection if semisimple.
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math.DG 1years
2026 1verdicts
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Star-Shaped Nakajima Quiver Varieties, Parabolic Higgs Bundle Moduli Spaces, and their Holomorphic Symplectic Structures
A stability-preserving map T from star-shaped Nakajima quiver varieties to central-Levi parabolic Higgs bundle moduli spaces is a homeomorphism on the trivial holomorphic structure locus and identifies their holomorphic symplectic structures.