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Title: Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
Authors: Mochizuki, Takuro  kyouindb  KAKEN_id
Author's alias: 望月, 拓郎
Keywords: harmonic bundle
asymptotic behaviour
asymptotic decoupling
Hitchin WKB-problem
limiting con guration
Hermitian-Einstein metric
Issue Date: Dec-2016
Publisher: John Wiley & Sons Inc
Journal title: Journal of Topology
Volume: 9
Issue: 4
Start page: 1021
End page: 1073
Abstract: Let (E, ∂E, θ) be a stable Higgs bundle of degree 0 on a compact connected Riemann surface. Once we fix a flat metric hdet(E) on the determinant of E, we have the harmonicmetrics ht (t > 0) for the stable Higgs bundles (E, ∂E, tθ) such that det(ht) = hdet(E).We study the behaviour of ht when t goes to ∞. First, we show that the Hitchin equation is asymptotically decoupled under the assumption that the Higgs field is generically regular semisimple. We apply it to the study of the so-called Hitchin Wentzel, Kramers, and Brillouin-problem. Secondly, we study the convergence of the sequence (E, ∂E, θ, ht) in the case rank E = 2. We introduce a rule to determine the parabolic weights of a 'limiting configuration', and we show the convergence of the sequence to the limiting configuration in an appropriate sense. The results can be appropriately generalized in the context of Higgs bundles with a Hermitian-Einstein metric on curves.
Rights: This is the peer reviewed version of the following article: [Mochizuki, T. (2016), Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces. Journal of Topology, 9: 1021–1073], which has been published in final form at https://doi.org/10.1112/jtopol/jtw018. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
The full-text file will be made open to the public on 1 SEP 2017 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
URI: http://hdl.handle.net/2433/227916
DOI(Published Version): 10.1112/jtopol/jtw018
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