Constructing Superelliptic Curves with non-trivial rational Torsion on\n their Jacobians

2017/07/13 by Max Kronberg, Kronberg, Max
Mathematics · Physics and Astronomy · #11G30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1707.04042

openalex publication_date 2017/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we describe the construction of superelliptic curves with a\nrational point of prescribed order on their jacobians. The construction is\nbased on Hensel's Lemma and produces for a given integer N a superelliptic\ncurve of genus linear in N with a rational N-division point on the\njacobian. The method is illustrated with multiple examples.\n

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