Analytic convergence of harmonic metrics for parabolic Higgs bundles

Semin Kim; Graeme Wilkin

doi:10.1016/j.geomphys.2018.01.023

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arXiv · 1705.08065

Analytic convergence of harmonic metrics for parabolic Higgs bundles

Semin Kim·Graeme Wilkin

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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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Semin Kim, Graeme Wilkin. 2017-05-23. Analytic convergence of harmonic metrics for parabolic Higgs bundles. https://doi.org/10.1016/j.geomphys.2018.01.023

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