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arXiv · 2403.07258

Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section

Hitoshi Fujioka
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Abstract

Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-sheeted branched covering of the Riemann surface. In particular, we give a condition for Higgs bundles in the Hitchin section on $\mathbb{C}$ or $\mathbb{C}^*$ to have compatible harmonic metrics.

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Hitoshi Fujioka. 2024-03-12. Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. https://doi.org/10.3842/sigma.2024.111

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