Reduction of Plane Quartics and Cayley Octads

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2025-06-02 DOI:10.1007/s10208-025-09704-y

Raymond van Bommel, Jordan Docking, Vladimir Dokchitser, Reynald Lercier, Elisa Lorenzo García

引用次数: 0

Abstract

We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p-adic criteria that efficiently give the stable reduction type amongst the 42 possible types, and whether the reduction is hyperelliptic or not. These criteria are in the vein of the machinery of “cluster pictures” for hyperelliptic curves. We also construct explicit families of quartic curves that realise all possible stable types, against which we test these criteria. We give numerical examples that illustrate how to use these criteria in practice.

查看原文本刊更多论文

平面四分位和Cayley八分位的约化

我们给出了局部场上平面四分体在Cayley八元上的稳定约简的一个推测特征。这导致p进准则有效地给出42种可能类型中的稳定约简类型，以及约简是否是超椭圆的。这些标准与超椭圆曲线的“星团图”机制是一致的。我们还构造了显式的四次曲线族，实现了所有可能的稳定类型，并对这些标准进行了测试。我们给出了数值例子来说明如何在实际中使用这些准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.