Ends of the moduli space of Higgs bundles

Mazzeo, Rafe; Swoboda, Jan; Weiss, Hartmut and Witt, Frederik (2016): Ends of the moduli space of Higgs bundles. In: Duke Mathematical Journal, Vol. 165, No. 12: pp. 2227-2271

Abstract

We associate to each stable Higgs pair (A(0), Phi(0)) on a compact Riemann surface X a singular limiting configuration (A(infinity), Phi(infinity)), assuming that 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 -> infinity. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0012-7094
• Language: English