Cyclic Cubic Points on Higher Genus Curves

2024/05/22 by James Rawson, Rawson, James
Computer Science · Mathematics · #11G30 #11G35 #14G05 #14H25 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2405.13743

openalex publication_date 2024/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The distribution of degree d points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: d = 3. For curves of genus at least 5, we show cubic points with Galois group C₃ arise from well-structured morphisms, along with providing computable tests for the existence of such morphisms. We prove the same for curves of lower genus under some geometric or arithmetic assumptions.

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