Ends of the moduli space of Higgs bundles

Abstract

We associate to each stable Higgs pair $(A_0,{\Phi }_0)$ on a compact Riemann surface $X$ a singular limiting configuration $(A_{\infty },{\Phi }_{\infty })$, assuming that $\det \Phi$ has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions $(A_t,t{\Phi }_t)$ to Hitchin's equations which converge to this limiting configuration as $t\to \infty$. This provides a new proof, via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space.

42 pages, minor revision

References in corpus (1)

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4

Cited by in corpus (29)

• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
• Asymptotics of certain families of Higgs bundles in the Hitchin component
• An Introduction to Higgs Bundles via Harmonic Maps
• Maximal representations, non Archimedean Siegel spaces, and buildings
• Asymptotic Geometry of the Hitchin Metric
• Singular Geometry and Higgs Bundles in String Theory
• On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces
• Exponential Decay for the Asymptotic Geometry of the Hitchin Metric
• From $S^1$-fixed points to $\mathcal{W}$-algebra representations
• Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles
• Adiabatic limits and Kazdan-Warner equations
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Generic Ends of the Moduli Space of $SL(n,\mathbb{C})$-Higgs Bundles
• Simpson-Mochizuki Correspondence for $\lambda$-Flat Bundles
• On Higgs Bundles on Nodal Curves
• Twisted cyclic quiver varieties on curves
• Higgs bundles, harmonic maps, and pleated surfaces
• Model Higgs bundles in exceptional components of the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety
• Hyperkähler metrics on the moduli space of weakly parabolic Higgs bundles
• Nilpotent Higgs bundles and families of flat connections
• The Algebraic and Analytic Compactifications of the Hitchin Moduli Space
• The behavior of sequences of solutions to the Hitchin-Simpson equations
• Reduction for $SL(3)$ pre-buildings
• Nonabelian Probes In Holography
• Affine special Kaehler structures in real dimension two
• $\mathfrak{sl}(2)$-type singular fibres of the symplectic and odd orthogonal Hitchin system
• The Hitchin fibration under degenerations to noded Riemann surfaces
• Sectional curvature asymptotics of the Higgs bundle moduli space