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arXiv · 2005.09706

Triples of rational points on the Hermitian curve and their Weierstrass semigroups

Gretchen L. Matthews·Dane Skabelund·Michael Wills
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Abstract

In this paper, we study configurations of three rational points on the Hermitian curve over $\mathbb{F}_{q^2}$ and classify them according to their Weierstrass semigroups. For $q>3$, we show that the number of distinct semigroups of this form is equal to the number of positive divisors of $q+1$ and give an explicit description of the Weierstrass semigroup for each triple of points studied. To do so, we make use of two-point discrepancies and derive a criterion which applies to arbitrary curves over a finite field.

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Gretchen L. Matthews, Dane Skabelund, Michael Wills. 2020-05-19. Triples of rational points on the Hermitian curve and their Weierstrass semigroups. https://arxiv.org/abs/2005.09706

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