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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.03436 |
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| _version_ | 1866911302833668096 |
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| author | Shu, Cheng |
| author_facet | Shu, Cheng |
| contents | For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities, and classify the connected components that admit symplectic resolutions. When $g>1$, we use elliptic endoscopic groups to control the singularities caused by irreducible local systems with automorphism groups larger than the centre of $G$; when $g=1$, our analysis is based on some results of Borel-Friedman-Morgan. The main results for $g>1$ were obtained by Herbig-Schwarz-Seaton via a different approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularities of character varieties Shu, Cheng Algebraic Geometry For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities, and classify the connected components that admit symplectic resolutions. When $g>1$, we use elliptic endoscopic groups to control the singularities caused by irreducible local systems with automorphism groups larger than the centre of $G$; when $g=1$, our analysis is based on some results of Borel-Friedman-Morgan. The main results for $g>1$ were obtained by Herbig-Schwarz-Seaton via a different approach. |
| title | Singularities of character varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.03436 |