Parabolic Hitchin Maps and Their Generic Fibers

2019/06/11 by Xiaoyu Su, Bin Wang, Su, Xiaoyu +3 · 2 citations
Mathematics · Physics and Astronomy · #14D20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1906.04475

openalex publication_date 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We set up a BNR correspondence for moduli spaces of Higgs bundles over a curve with a parabolic structure over any algebraically closed field. This leads to a concrete description of generic fibers of the associated strongly parabolic Hitchin map. We also show that the global nilpotent cone is equi-dimensional with half dimension of the total space. As a result, we prove the flatness and surjectivity of this map and the existence of very stable parabolic vector bundles.

Citations

• The Self-Duality Equations on a Riemann Surface

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