2014/09/30 by Nazar Arakelian, Arakelian, Nazar, Herivelto Borges +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.1409.8549
arxiv created 2014/09/30 · openalex publication_date 2014/09/30 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each integer s≥ 1, we present a family of curves that are \mathbbFq-Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s = 2, we give necessary and sufficient conditions for such curves to be \mathbbFq-Frobenius nonclassical with respect to the linear system of conics. In the \mathbbFq-Frobenius nonclassical cases, we determine the exact number of \mathbbFq-rational points. In the remaining cases, an upper bound for the number of \mathbbFq-rational points will follow from Stöhr-Voloch theory.