An unusual family of supersingular curves of genus five in characteristic two

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-10-10 DOI:10.1016/j.ffa.2025.102736

Dušan Dragutinović

引用次数: 0

Abstract

We construct a family of smooth supersingular curves of genus 5 in characteristic 2 with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus 5, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-2 curve. We also provide an explicit parametrization of this family.

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特征二的五属超奇异曲线的一个不寻常的族

构造了特征2上的5属光滑超奇异曲线族，它的维数与5属超奇异轨迹的任意分量的期望维数相匹配，它的成员是具有非平凡自同构群的非超椭圆曲线，族中的每条曲线都在椭圆曲线和2属曲线上具有双覆盖结构。我们还提供了这个家族的显式参数化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.