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Choosing points on cubic plane curves: rigidity and flexibility

Ishan Banerjee Weiyan Chen

Algebraic Geometry mathscidoc:2204.45033

2021.3
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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@inproceedings{ishan2021choosing,
  title={Choosing points on cubic plane curves: rigidity and flexibility},
  author={Ishan Banerjee, and Weiyan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428141953776797146},
  year={2021},
}
Ishan Banerjee, and Weiyan Chen. Choosing points on cubic plane curves: rigidity and flexibility. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428141953776797146.
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