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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07136 |
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| _version_ | 1866929534192844800 |
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| author | Hidalgo, Ruben A. |
| author_facet | Hidalgo, Ruben A. |
| contents | The configuration space of $k \geq 3$ ordered points in the Riemann sphere $\widehat{\mathbb C}$ is the Torelli space ${\mathcal U}_{0,k}$; a complex manifold of dimension $k-3$. If $m,n \geq 4$ and $F:{\mathcal U}_{0,m} \to {\mathcal U}_{0,n}$ is a non-constant holomorphic map, then we observe that (i) $n \leq m$ and (ii) each coordinate of $F$ is given by a cross-ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07136 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple remark on holomorphic maps on Torelli space of marked spheres Hidalgo, Ruben A. Complex Variables The configuration space of $k \geq 3$ ordered points in the Riemann sphere $\widehat{\mathbb C}$ is the Torelli space ${\mathcal U}_{0,k}$; a complex manifold of dimension $k-3$. If $m,n \geq 4$ and $F:{\mathcal U}_{0,m} \to {\mathcal U}_{0,n}$ is a non-constant holomorphic map, then we observe that (i) $n \leq m$ and (ii) each coordinate of $F$ is given by a cross-ratio. |
| title | A simple remark on holomorphic maps on Torelli space of marked spheres |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2410.07136 |