Uniformization of branched surfaces and Higgs bundles

Author:

Biswas Indranil1,Bradlow Steven2,Dumitrescu Sorin3ORCID,Heller Sebastian4

Affiliation:

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

3. Université Côte d’Azur, CNRS, LJAD, France

4. Institute of Differential Geometry, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Abstract

Given a compact connected Riemann surface [Formula: see text] of genus [Formula: see text], and an effective divisor [Formula: see text] on [Formula: see text] with [Formula: see text], there is a unique cone metric on [Formula: see text] of constant negative curvature [Formula: see text] such that the cone angle at each point [Formula: see text] is [Formula: see text] [R. C. McOwen, Point singularities and conformal metrics on Riemann surfaces, Proc. Amer. Math. Soc. 103 (1988) 222–224; M. Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991) 793–821]. We describe the Higgs bundle on [Formula: see text] corresponding to the uniformization associated to this conical metric. We also give a family of Higgs bundles on [Formula: see text] parametrized by a nonempty open subset of [Formula: see text] that correspond to conical metrics of the above type on moving Riemann surfaces. These are inspired by Hitchin’s results in [N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59–126] for the case [Formula: see text].

Funder

DFG

National Research Agency

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Conformal Limit and Projective Structures;International Mathematics Research Notices;2024-07-03

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