Choosing points on cubic plane curves: rigidity and flexibility
Algebraic Geometry
2024-11-04 v3 Geometric Topology
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 distinct points on every smooth cubic plane curve, for each given positive integer ? We give an affirmative answer to the question when and 18 (the smallest open cases), and a negative answer for infinitely many 's.
Cite
@article{arxiv.2101.03824,
title = {Choosing points on cubic plane curves: rigidity and flexibility},
author = {Ishan Banerjee and Weiyan Chen},
journal= {arXiv preprint arXiv:2101.03824},
year = {2024}
}
Comments
35 pages, 4 figures. An Appendix was added to the second version, recording a related result that we learned from Curtis McMullen