For locally fiducial SL(2,C)-Higgs bundles over singular spectral curves, Hitchin equation solutions and the restricted Hitchin metric converge exponentially to semi-flat data along the large-Higgs-field ray.
Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case
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abstract
We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero degree case, we introduce the semi-flat metric, and compare the asymptotic behaviour of the semi-flat metric and the Hitchin metric along the ray $(E,t\theta)$ $(t\to\infty)$.
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The asymptotics of the $\mathrm{SL}_2(\mathbb{C})$-Hitchin metric on the singular locus: subintegrable systems
For locally fiducial SL(2,C)-Higgs bundles over singular spectral curves, Hitchin equation solutions and the restricted Hitchin metric converge exponentially to semi-flat data along the large-Higgs-field ray.