具有许多有理点且亏格与维数较小的三元与四元曲线
数论
2022-05-03 v2
摘要
我们将之前论文 arXiv:2005.07054 中的计算扩展至确定 与 上固定维数（gonality）且小亏格曲线上有理点的最大数量。例如，我们发现有限域上不存在亏格5且维数6的曲线。我们基于数据提出两个猜想。第一，亏格为 的最优曲线其维数至多为 。第二， 上维数为 且大亏格的曲线具有 个有理点。
引用
@article{arxiv.2010.07992,
title = {Ternary and Quaternary Curves of Small Fixed Genus and Gonality with Many Rational Points},
author = {Xander Faber and Jon Grantham},
journal= {arXiv preprint arXiv:2010.07992},
year = {2022}
}
备注
Final published version as it will appear in Experimental Mathematics; 19 pages; code available at https://github.com/RationalPoint/gonality [Note that an error was corrected since the previous version: up to isomorphism, there is exactly 1 curve of genus 4 and gonality 5 over GF(3).]