论文标题
小固定属和高态的三元和第四纪曲线，有许多合理的点
Ternary and Quaternary Curves of Small Fixed Genus and Gonality with Many Rational Points
论文作者
论文摘要
我们从以前的论文ARXIV：2005.07054扩展了计算，以确定曲线上的最大理性点数量超过$ \ Mathbb {f} _3 $和$ \ Mathbb {f} _4 $，带有固定的gonality and Gonality and Genus。例如，我们发现在有限场上没有第5属和Gonality 6的曲线。我们根据我们的数据提出了两个猜想。首先，最佳属$ g $的最佳曲线最多具有$ \ lfloor \ frac {g+3} {2} {2} \ rfloor $。其次，$ \ mathbb {f} _q $的gonality $γ$和大属的曲线具有$γ（q+1）$合理点。
We extend the computations from our previous paper arXiv:2005.07054 to determine the maximum number of rational points on a curve over $\mathbb{F}_3$ and $\mathbb{F}_4$ with fixed gonality and small genus. We find, for example, that there is no curve of genus 5 and gonality 6 over a finite field. We propose two conjectures based on our data. First, an optimal curve of genus $g$ has gonality at most $\lfloor \frac{g+3}{2} \rfloor$. Second, a curve of gonality $γ$ and large genus over $\mathbb{F}_q$ has $γ(q+1)$ rational points.
