Sectional curvature asymptotics of the Higgs bundle moduli space

2017/01/12 by Jan Swoboda, Swoboda, Jan
Mathematics · #53C07 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1701.03293

openalex publication_date 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the asymptotic behavior in the limit of large Higgs fields of the sectional curvatures of the natural L² hyperkähler metric G_L² of the moduli space \mathcal M of rank-2 Higgs bundles on a Riemann surface Σ away from the discriminant locus. It is shown that their leading order part is given by a sum of Dirac type contributions on Σ, for which we find explicit expressions.

Citations

• The Self-Duality Equations on a Riemann Surface

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