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arXiv · 2607.00818

A realizability criterion for rational maps with three branch points

Zhiqiang Wei
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Abstract

Let \[ \pi_{0}=[\underbrace{2,\ldots,2}_{2s-1}],\quad \pi_{\infty}=[\underbrace{3,\ldots,3}_{s},\underbrace{1,\ldots,1}_{s-2}],\quad \pi_{1}=[\gamma_{1},\gamma_{2},\gamma_{3}] \] be three nontrivial partitions of the integer \(d=4s-2\), where \(s\ge 3\). We establish a necessary and sufficient condition for the candidate datum \(\{\pi_{0},\pi_{\infty},\pi_{1}\}\) to be realizable by a rational map.

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Zhiqiang Wei. 2026-07-01. A realizability criterion for rational maps with three branch points. https://arxiv.org/abs/2607.00818

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