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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.
Forward citations
Cited by 2 Pith papers
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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 holomorph...
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The asymptotics of the $\mathrm{SL}_2(\mathbb{C})$-Hitchin metric on the singular locus: subintegrable systems
For locally fiducial SL(2,C)-Higgs bundles over singular spectral curves, Hitchin equation solutions and the restricted Hitchin metric converge exponentially to semi-flat data along the large-Higgs-field ray.
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