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arXiv · 2607.14128

Rigidity of multisections to the universal cubic plane curve

Jinwen Yao
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Abstract

We study the following question of Farb: For which positive integers n is it possible to choose n distinct points continuously on every smooth cubic plane curve? This paper is a continuation of the work of Banerjee-Chen. We prove that such choice is unique up to homotopy for n=27 (smallest open case), and does not exist for n=36k+18.

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Jinwen Yao. 2026-06-20. Rigidity of multisections to the universal cubic plane curve. https://arxiv.org/abs/2607.14128

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