Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case

2025/01/22 by Takuro Mochizuki, Mochizuki, Takuro
Mathematics · Physics and Astronomy · #14D21 #53C07 #58E15 #81T13 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2501.12741

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero degree case, we introduce the semi-flat metric, and compare the asymptotic behaviour of the semi-flat metric and the Hitchin metric along the ray (E,tθ) (t→∞).

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• Generic Ends of the Moduli Space of SL(n,ℂ)-Higgs Bundles
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