PreprintCC BY 4.0arXiv
Rigidity of multisections to the universal cubic plane curve
Abstract
We study the following question of Farb: For which positive integers n is it possible to choose n distinct points continuously on every smooth cubic plane curve? This paper is a continuation of the work of Banerjee-Chen. We prove that such choice is unique up to homotopy for n=27 (smallest open case), and does not exist for n=36k+18.
Related
- Nonexistence of degree two rational multisections of conic bundles over the plane
- A Sarkisov Involution from a Rational Cubic Curve on a Quartic Double Solid
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- Cubic Progressions on Smooth Plane Curves
- Fermat's Last Theorem in star-invariant subspaces II: small boundary spectrum, projective plane curves, and the cubic Fermat equation
BibTeX
@misc{yao2026rigidity,
title = {{Rigidity of multisections to the universal cubic plane curve}},
author = {Jinwen Yao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14128},
eprint = {2607.14128},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14128},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rigidity of multisections to the universal cubic plane curve
AU - Jinwen Yao
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.14128
UR - https://arxiv.org/abs/2607.14128
AB - We study the following question of Farb: For which positive integers n is it possible to choose n distinct points continuously on every smooth cubic plane curve? This paper is a continuation of the work of Banerjee-Chen. We prove that such choice is unique up to homotopy for n=27 (smallest open case), and does not exist for n=36k+18.
ER -