Compact relative SO₀(2,q)-character varieties of punctured spheres

2023/09/27 by Feng, Yu, Zhang, Junming
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.15553

Abstract

We prove that there are relative SO₀(2,q)-character varieties of the punctured sphere which are compact, totally non-hyperbolic and contain a dense representation. This work fills a remaining case of the results of N. Tholozan and J. Toulisse. Our approach relies on the non-abelian Hodge correspondence and we study the moduli space of parabolic SO₀(2,q)-Higgs bundles with some fixed weight. Additionally, we provide a construction based on Geometric Invariant Theory (GIT) to demonstrate that the considered moduli spaces can be viewed as a projective variety over ℂ.

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