A simple remark on holomorphic maps on Torelli space of marked spheres

Ruben A. Hidalgo

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arXiv · 2410.07136

A simple remark on holomorphic maps on Torelli space of marked spheres

Ruben A. Hidalgo

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Abstract

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.

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Ruben A. Hidalgo. 2024-10-09. A simple remark on holomorphic maps on Torelli space of marked spheres. https://arxiv.org/abs/2410.07136

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