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1 September 2016 Ends of the moduli space of Higgs bundles
Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, Frederik Witt
Duke Math. J. 165(12): 2227-2271 (1 September 2016). DOI: 10.1215/00127094-3476914

Abstract

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.

Citation

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Rafe Mazzeo. Jan Swoboda. Hartmut Weiss. Frederik Witt. "Ends of the moduli space of Higgs bundles." Duke Math. J. 165 (12) 2227 - 2271, 1 September 2016. https://doi.org/10.1215/00127094-3476914

Information

Received: 8 July 2014; Revised: 9 August 2015; Published: 1 September 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1352.53018
MathSciNet: MR3544281
Digital Object Identifier: 10.1215/00127094-3476914

Subjects:
Primary: 53C07
Secondary: 35J05

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 12 • 1 September 2016
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