论文标题
Skabelund最大曲线上的Weierstrass半群
Weierstrass semigroups on the Skabelund maximal curve
论文作者
论文摘要
在2017年，D。Skabelund在$ \ Mathbb {f} _ {q^4} $上构建了最大曲线，作为Suzuki Curve的环状盖。在本文中，我们明确确定了Skabelund曲线的任何时候Weierstrass Semigroup的结构。我们证明其WeierStrass点正是$ \ Mathbb {f} _ {q^4} $ - 有理点。我们还表明，在Weierstrass点中，出现了两种类型的Weierstrass Semigroup：一种用于$ \ Mathbb {f} _Q $ - 理性点，其中一种用于其余$ \ Mathbb {f} _ {q^4} $ - 理性点。对于这两种类型中的每一种，它的Apéry集合以及一组发电机都被计算出来。
In 2017, D. Skabelund constructed a maximal curve over $\mathbb{F}_{q^4}$ as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point $P$ of the Skabelund curve. We show that its Weierstrass points are precisely the $\mathbb{F}_{q^4}$-rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the $\mathbb{F}_q$-rational points, one for the remaining $\mathbb{F}_{q^4}$-rational points. For each of these two types its Apéry set is computed as well as a set of generators.
