论文标题
部分可观测时空混沌系统的无模型预测
On abelian covers of the projective line with fixed gonality and many rational points
论文作者
论文摘要
在有限字段$ \ mathbb {f} _q $带gonality $γ$上的平滑几何连接曲线最多具有$ {γ（q+1）} $合理点。第一作者和格兰瑟姆（Grantham）猜想，每个足够大的属的曲线都有达到这一界限的gonality $γ$。在本文中，我们表明，使用射影线的Abelian封面可以实现无限序列的属性。我们还认为，阿贝利亚的封面不足以证明全部猜想。
A smooth geometrically connected curve over the finite field $\mathbb{F}_q$ with gonality $γ$ has at most ${γ(q+1)}$ rational points. The first author and Grantham conjectured that there exist curves of every sufficiently large genus with gonality $γ$ that achieve this bound. In this paper, we show that this bound can be achieved for an infinite sequence of genera using abelian covers of the projective line. We also argue that abelian covers will not suffice to prove the full conjecture.
