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

2023/03/08 by Mochizuki, Takuro, Szabó, Szilárd · 1 citation
#14D21 #53C07 #58E15 #81T13 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.04913

Abstract

Let X be a compact Riemann surface. Let (E,θ) be a stable Higgs bundle of degree 0 on X. Let h_det(E) denote a flat metric of the determinant bundle det(E). For any t>0, there exists a unique harmonic metric h_t of (E,θ) such that det(h_t)=h_det(E). We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence h_t 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.

Cited by

• The asymptotics of the SL₂(ℂ)-Hitchin metric on the singular locus: subintegrable systems

Related

• Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles
• Comparison of the Hitchin metric and the semi-flat metric in the rank two case
• The asymptotics of the SL₂(ℂ)-Hitchin metric on the singular locus: subintegrable systems
• Limiting configurations for the SU(1,2) Hitchin equation
• Asymptotic Geometry of the Moduli Space of Rank Two Irregular Higgs Bundles over the Projective Line