Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres

Yu Feng; Junming Zhang

Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres

Differential Geometry 2025-09-19 v2 Algebraic Geometry

Authors: Yu Feng , Junming Zhang

Abstract

We prove that there are relative $\mathrm{SO}_0(2,q)$ -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 $\mathrm{SO}_0(2,q)$ -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 $\mathbb{C}$ .

Keywords

character varieties punctured sphere so(2,q) higgs bundles non-abelian hodge correspondence geometric invariant theory

Cite

@article{arxiv.2309.15553,
  title  = {Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres},
  author = {Yu Feng and Junming Zhang},
  journal= {arXiv preprint arXiv:2309.15553},
  year   = {2025}
}

Comments

Final version, to appear in Annals of Global Analysis and Geometry. 39 pages, comments are very welcome

Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres

Abstract

Keywords

Cite

Comments

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