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arXiv · 1811.09224

The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines

Nazar Arakelian·Herivelto Borges·Pietro Speziali
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Abstract

For any smooth Hurwitz curve $\mathcal{H}_n: \, XY^n+YZ^n+X^nZ=0$ over the finite field $\mathbb{F}_{p}$, an explict description of its Weierstrass points for the morphism of lines is presented. As a consequence, the full automorphism group ${\rm Aut}(\mathcal{H}_n)$, as well as the genera of all Galois subcovers of $\mathcal{H}_n$, with $n\neq 3, p^r$, are computed. Finally, a question by F. Torres on plane non nonsingular maximal curves is answered.

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Nazar Arakelian, Herivelto Borges, Pietro Speziali. 2018-11-22. The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines. https://arxiv.org/abs/1811.09224

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