Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles

Takuro Mochizuki

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arXiv · 2305.17638

Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles

Takuro Mochizuki

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Abstract

The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperk\"ahler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperk\"ahler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray $(E,t\theta)$ as $t\to\infty$.

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Takuro Mochizuki. 2023-05-28. Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles. https://arxiv.org/abs/2305.17638

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