Analytic convergence of harmonic metrics for parabolic Higgs bundles
Analytic convergence of harmonic metrics for parabolic Higgs bundles
复制标题
抛物线希格斯丛的调和度量的解析收敛
DOI：
10.1016/j.geomphys.2018.01.023
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发表时间：
2017
影响因子：
1.5
通讯作者：
Graeme Wilkin
中科院分区：
文献类型：
--
作者：
Semin Kim;Graeme Wilkin
本文研究了刺穿黎曼曲面上的抛物希格斯束的模空间，这些束在刺穿处具有不同的权值。我们证明了谐波度规解析地依赖于权重和稳定希格斯束。给出了McOwen关于在给定保形类中穿孔表面上双曲锥度量存在性的定理的希格斯束推广，以及Judge关于这些度量的解析参数化的定理的推广。
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.