Topological complexity of finding flex points on cubic plane curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866918131581059072 |
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| author | Chen, Weiyan Wan, Zheyan |
| author_facet | Chen, Weiyan Wan, Zheyan |
| contents | We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus of a cover associated to this problem. We also show that our lower bound for the complexity is close to be the best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17303 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological complexity of finding flex points on cubic plane curves Chen, Weiyan Wan, Zheyan Geometric Topology Algebraic Geometry Algebraic Topology 55R80, 55M30 We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus of a cover associated to this problem. We also show that our lower bound for the complexity is close to be the best possible. |
| title | Topological complexity of finding flex points on cubic plane curves |
| topic | Geometric Topology Algebraic Geometry Algebraic Topology 55R80, 55M30 |
| url | https://arxiv.org/abs/2306.17303 |