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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16877 |
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| _version_ | 1866915806025089024 |
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| author | Lennen, Emmett |
| author_facet | Lennen, Emmett |
| contents | We consider relative character varieties on $\mathbb{P}^1\backslash\{0,1,\infty\}$ with $G=GL(r), O(r)$, or $Sp(r)$. Using a diagrammatic method of Simpson's, we give an explicit linear upper bound $R(d)$ on the rank $r$ of an MC-minimal character variety of dimension $d>2$. An arbitrary character variety is isomorphic, via Katz's middle convolution, to one satisfying the bound. For the general linear and non-overlapping quadratic cases, the bounds we give are the sharpest possible using this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension bounds for relative character varieties on the projective line with three punctures $G=GL(r), O(r), Sp(r)$ Lennen, Emmett Algebraic Geometry 14M35 We consider relative character varieties on $\mathbb{P}^1\backslash\{0,1,\infty\}$ with $G=GL(r), O(r)$, or $Sp(r)$. Using a diagrammatic method of Simpson's, we give an explicit linear upper bound $R(d)$ on the rank $r$ of an MC-minimal character variety of dimension $d>2$. An arbitrary character variety is isomorphic, via Katz's middle convolution, to one satisfying the bound. For the general linear and non-overlapping quadratic cases, the bounds we give are the sharpest possible using this method. |
| title | Dimension bounds for relative character varieties on the projective line with three punctures $G=GL(r), O(r), Sp(r)$ |
| topic | Algebraic Geometry 14M35 |
| url | https://arxiv.org/abs/2602.16877 |