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


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.


Download Citation

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


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

Primary: 53C07
Secondary: 35J05

Keywords: Higgs bundles , Hitchin’s equations , limiting configurations

Rights: Copyright © 2016 Duke University Press

Vol.165 • No. 12 • 1 September 2016
Back to Top