Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 12 (2016), 2227-2271.
Ends of the moduli space of Higgs bundles
We associate to each stable Higgs pair on a compact Riemann surface a singular limiting configuration , assuming that has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions to Hitchin’s equations, which converge to this limiting configuration as . 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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