Analytic convergence of harmonic metrics for parabolic Higgs bundles

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JournalJournal of Geometry and Physics
DateAccepted/In press - 24 Jan 2018
DateE-pub ahead of print - 3 Feb 2018
DatePublished (current) - 1 Apr 2018
Volume127
Number of pages13
Pages (from-to)55-67
Early online date3/02/18
Original languageEnglish

Abstract

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the existence of hyperbolic cone metrics on a punctured surface within a given conformal class, and a generalisation of a theorem of Judge on the analytic parametrisation of these metrics.

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