Obstructions to choosing distinct points on cubic plane curves
Geometric Topology
2019-02-12 v2 Algebraic Geometry
Abstract
Every smooth cubic plane curve has 9 inflection points, 27 sextatic points, and 72 ``points of type nine". Motivated by these classical algebro-geometric constructions, we study the following topological question: Is it possible to continuously choose distinct unordered points on each smooth cubic plane curve for a natural number ? This question is equivalent to asking if certain fiber bundle admits a continuous section or not. We prove that the answer is no when is not a multiple of 9. Our result resolves a conjecture of Benson Farb.
Cite
@article{arxiv.1806.10207,
title = {Obstructions to choosing distinct points on cubic plane curves},
author = {Weiyan Chen},
journal= {arXiv preprint arXiv:1806.10207},
year = {2019}
}
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