Asymptotic Geometry of the Moduli Space of Rank Two Irregular Higgs Bundles over the Projective Line

2022/06/23 by Gao Chen, Chen, Gao, Nianzi Li +1 · 1 citation
Mathematics · Physics and Astronomy · #53C07 #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2206.11883

openalex publication_date 2022/06/23 · openalex created_date 2022/06/26 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of Hitchin's hyperkähler metric on the moduli space of rank two irregular Higgs bundles over ℂP¹. Along a generic curve, we prove that the Hitchin metric is asymptotic to the semiflat metric at an arbitrary polynomial order. When there are no weakly parabolic singularities, the rate is exponential. In the case of four-dimensional moduli spaces, we prove that the semiflat metric is asymptotic to an ALG/ALG^∗ model metric.

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

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