The Asymptotics of Representations for Cyclic Opers

2016/09/20 by J.M. Rojas Acosta, Acosta, Jorge
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1609.06343

openalex publication_date 2016/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Riemann surface X = (Σ, J) we find an expression for the dominant term for the asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form (0,0,⋯,tω_n). Moreover, we find an associated equivariant map from the universal cover (Σ,J) to the symmetric space SL_n(ℂ) / SU(n) and show that limits of these maps tend to a sub-building in the asymptotic cone. That sub-building is explicitly constructed from the local data of ω_n.

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