2021/05/11 by Masaaki Homma, Homma, Masaaki
Computer Science · Mathematics · #05B25 #11G20 #14G05 #14G15 #14H50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2105.04784
openalex publication_date 2021/05/11 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
The classification of maximal plane curves of degree 3 over \mathbbF4 will be given, which complements Hirschfeld-Storme-Thas-Voloch's theorem on a characterization of Hermitian curves in ℙ2. This complementary part should be understood as the classification of Sziklai's example of maximal plane curves of degree q-1 over \mathbbFq. Although two maximal plane curves of degree 3 over \mathbbF4 up to projective equivalence over \mathbbF4 appear, they are birationally equivalent over \mathbbF4 each other.