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Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case

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arxiv 2501.12741 v1 pith:R7LEFN4N submitted 2025-01-22 math.AG

Takuro Mochizuki This is my paper · ORCID
classification math.AG
keywords metricsemi-flatcasedegreehiggshitchinnon-zerosmooth
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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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  1. The asymptotics of the $\mathrm{SL}_2(\mathbb{C})$-Hitchin metric on the singular locus: subintegrable systems

    math.DG 2025-06 conditional novelty 6.0 of 10

    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.

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