Intersection of holonomy varieties of $CP^1$-structures
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911097098862592 |
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| author | Baba, Shinpei |
| author_facet | Baba, Shinpei |
| contents | Let $Σ$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $Σ$, possibly with opposite orientations.
In this paper, we show that there are (exactly) countably infinite pairs of ${\rm CP}^1$-structures on $X$ and on $Y$ sharing holonomy $π_1(Σ) \to {\rm PSL}_2 {\rm C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection of holonomy varieties of $CP^1$-structures Baba, Shinpei Geometric Topology Complex Variables Differential Geometry Let $Σ$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $Σ$, possibly with opposite orientations. In this paper, we show that there are (exactly) countably infinite pairs of ${\rm CP}^1$-structures on $X$ and on $Y$ sharing holonomy $π_1(Σ) \to {\rm PSL}_2 {\rm C}$. |
| title | Intersection of holonomy varieties of $CP^1$-structures |
| topic | Geometric Topology Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2502.11322 |