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Main Author: Hidalgo, Ruben A.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.07136
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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