Cyclic cubic points on higher genus curves

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-11 DOI:10.1112/jlms.70288

James Rawson

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引用次数: 0

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 $C_{3}$ 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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高属曲线上的循环三次点

d$ d$点在曲线上的分布很好理解，特别是对于低度。我们改进了这项研究，在最简单有趣的情况下包括伽罗瓦群的信息：d = 3$ d = 3$。对于属至少为5的曲线，我们证明了伽罗瓦群c3 $C_3$的三次点是由结构良好的态射产生的，并给出了这种态射存在的可计算检验。在一些几何或算术假设下，我们证明了下格曲线的相同性质。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.