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arXiv · 2004.14726

Weierstrass semigroups on the Skabelund maximal curve

Peter Beelen·Leonardo Landi·Maria Montanucci
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Abstract

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 Ap\'ery set is computed as well as a set of generators.

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Peter Beelen, Leonardo Landi, Maria Montanucci. 2020-04-30. Weierstrass semigroups on the Skabelund maximal curve. https://arxiv.org/abs/2004.14726

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