Generic Ends of the Moduli Space of $SL(n,\mathbb{C})$-Higgs Bundles

Abstract

Given a generic ray of Higgs bundles $({\overline{\partial }}_E,t\phi )$, 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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Cited by in corpus (4)

• An Introduction to Higgs Bundles via Harmonic Maps
• Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• The behavior of sequences of solutions to the Hitchin-Simpson equations