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

Max Kronberg

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

Number Theory 2017-07-14 v1

Authors: Max Kronberg

Abstract

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

Keywords

superelliptic curves rational torsion Jacobians Hensel's lemma curve construction rational points genus

Cite

@article{arxiv.1707.04042,
  title  = {Constructing Superelliptic Curves with non-trivial rational Torsion on their Jacobians},
  author = {Max Kronberg},
  journal= {arXiv preprint arXiv:1707.04042},
  year   = {2017}
}

Comments

8 pages

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