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.
Generic Ends of the Moduli Space of $SL(n,\mathbb{C})$-Higgs Bundles
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abstract
Given a generic ray of Higgs bundles $(\overline{\partial}_E, t\varphi)$, we describe the corresponding family of hermitian metrics $h_t$ solving Hitchin's equations via gluing methods. In the process, we construct a family of approximate solutions $h_t^{\mathrm{app}}$ which differ from the actual harmonic metrics $h_t$ by error terms of size $\mathrm{e}^{-\delta t}$. Such families of explicit approximate solutions have already proved useful for answering finer questions about the asymptotic geometry of the Hitchin moduli space.
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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.