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arXiv · 2105.04784

On maximal plane curves of degree $3$ over $\mathbb{F}_4$,and Sziklai's example of degree $q-1$ over $\mathbb{F}_q$

Masaaki Homma
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Abstract

The classification of maximal plane curves of degree $3$ over $\mathbb{F}_4$ will be given, which complements Hirschfeld-Storme-Thas-Voloch's theorem on a characterization of Hermitian curves in $\mathbb{P}^2$. This complementary part should be understood as the classification of Sziklai's example of maximal plane curves of degree $q-1$ over $\mathbb{F}_q$. Although two maximal plane curves of degree $3$ over $\mathbb{F}_4$ up to projective equivalence over $\mathbb{F}_4$ appear, they are birationally equivalent over $\mathbb{F}_4$ each other.

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Masaaki Homma. 2021-05-11. On maximal plane curves of degree $3$ over $\mathbb{F}_4$,and Sziklai's example of degree $q-1$ over $\mathbb{F}_q$. https://arxiv.org/abs/2105.04784

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