Choosing points on cubic plane curves: rigidity and flexibility
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910679453138944 |
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| author | Banerjee, Ishan Chen, Weiyan |
| author_facet | Banerjee, Ishan Chen, Weiyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03824 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Choosing points on cubic plane curves: rigidity and flexibility Banerjee, Ishan Chen, Weiyan Algebraic Geometry Geometric Topology 55R10 (primary), 55R80, 14H50 (secondary) 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. |
| title | Choosing points on cubic plane curves: rigidity and flexibility |
| topic | Algebraic Geometry Geometric Topology 55R10 (primary), 55R80, 14H50 (secondary) |
| url | https://arxiv.org/abs/2101.03824 |