Duke Mathematical Journal

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 $\operatorname{det}\Phi$ 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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1473186400

Digital Object Identifier
doi:10.1215/00127094-3476914

Mathematical Reviews number (MathSciNet)
MR3544281

Zentralblatt MATH identifier
1352.53018

Citation

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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