Duke Mathematical Journal

Ends of the moduli space of Higgs bundles

Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, and Frederik Witt

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We associate to each stable Higgs pair (A0,Φ0) on a compact Riemann surface X a singular limiting configuration (A,Φ), assuming that detΦ has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions (At,tΦt) to Hitchin’s equations, which converge to this limiting configuration as t. 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.

Article information

Duke Math. J., Volume 165, Number 12 (2016), 2227-2271.

Received: 8 July 2014
Revised: 9 August 2015
First available in Project Euclid: 6 September 2016

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Zentralblatt MATH identifier

Primary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]
Secondary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]

Hitchin’s equations Higgs bundles limiting configurations


Mazzeo, Rafe; Swoboda, Jan; Weiss, Hartmut; Witt, Frederik. Ends of the moduli space of Higgs bundles. Duke Math. J. 165 (2016), no. 12, 2227--2271. doi:10.1215/00127094-3476914. https://projecteuclid.org/euclid.dmj/1473186400

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