Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908544426573824 |
|---|---|
| author | Feng, Yu Zhang, Junming |
| author_facet | Feng, Yu Zhang, Junming |
| contents | 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 $\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres Feng, Yu Zhang, Junming Differential Geometry Algebraic Geometry 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 $\mathbb{C}$. |
| title | Compact relative $\mathrm{SO}_0(2,q)$-character varieties of punctured spheres |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2309.15553 |