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Comparison of the Hitchin metric and the semi-flat metric in the rank two case

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arxiv 2407.05188 v1 pith:VAYQULOL submitted 2024-07-06 math.DG math.AG

Takuro Mochizuki This is my paper
classification math.DGmath.AG
keywords metricthetacurveexponentialhiggshitchinmetricsrank
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abstract

Let $(E,\theta)$ be a Higgs bundle of rank $2$ and degree $0$ on a compact Riemann surface $X$ whose spectral curve is smooth. The tangent space of the moduli space of Higgs bundles at $(E,\theta)$ is equipped with two natural metrics called the Hitchin metric and the semi-flat metric. It is known that the difference between two metrics along the curve $(E,t\theta)$ $(t\geq 1)$ decays in an exponential way. In this paper, we shall study how the exponential rate is improved.

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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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