Asymptotic behaviour of large-scale solutions of Hitchin’s equations in higher rank

Mochizuki, Takuro and Szabó, Szilárd (2025) Asymptotic behaviour of large-scale solutions of Hitchin’s equations in higher rank. Moduli, 2. ISSN 2949-7647

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Abstract

Let be a compact Riemann surface. Let be a stable Higgs bundle of degree on . Let denote a flat metric of the determinant bundle . For any , there exists a unique harmonic metric of such that . We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence is convergent to the naturally defined decoupled harmonic metric at the speed of the exponential order. We also obtain a uniform convergence for such a family of Higgs bundles.

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