可由Harbater-Katz-Gabber覆盖实现的最大曲线的Weierstrass半群

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2022-07-01 DOI:10.1515/advgeom-2022-0014

H. Charalambous, K. Karagiannis, Sotiris Karanikolopoulos, A. Kontogeorgis

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引用次数: 0

摘要

摘要给出了在有限域的代数闭包上定义的极大曲线可实现为hkg覆盖的充分必要条件。我们在曲线的有理点上使用极点数的方法。对于这类曲线，我们计算了它们的Weierstrass半群以及它们的高分支过滤在这一点(覆盖的唯一分支点)的跳变。

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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Weierstrass semigroups for maximal curves realizable as Harbater–Katz–Gabber covers

Abstract We present a necessary and sufficient condition for a maximal curve, defined over the algebraic closure of a finite field, to be realised as an HKG-cover. We use an approach via pole numbers in a rational point of the curve. For this class of curves, we compute their Weierstrass semigroup as well as the jumps of their higher ramification filtrations at this point, the unique ramification point of the cover.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.