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arXiv · 2101.03824

Choosing points on cubic plane curves: rigidity and flexibility

Ishan Banerjee·Weiyan Chen
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Abstract

Every smooth cubic plane curve has 9 flex points and 27 sextatic points. We study the following question asked by Farb: Is it true that the known algebraic structures give all the possible ways to continuously choose $n$ distinct points on every smooth cubic plane curve, for each given positive integer $n$? We give an affirmative answer to the question when $n=9$ and 18 (the smallest open cases), and a negative answer for infinitely many $n$'s.

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Ishan Banerjee, Weiyan Chen. 2021-01-11. Choosing points on cubic plane curves: rigidity and flexibility. https://doi.org/10.1016/j.aim.2023.108959

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