Weight bounds for $$(3,\gamma )$$ -hyperelliptic curves

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-02-05 DOI:10.1007/s10801-023-01295-7

引用次数: 0

Abstract

$(N,\gamma )$ -hyperelliptic semigroups were introduced by Fernando Torres to encapsulate the most salient properties of Weierstrass semigroups associated with totally ramified points of N-fold covers of curves of genus $\gamma $ . Torres characterized $(2,\gamma )$ -hyperelliptic semigroups of maximal weight whenever their genus is large relative to $\gamma $ . Here we do the same for $(3,\gamma )$ -hyperelliptic semigroups, and we formulate a conjecture about the general case whenever $N \ge 3$ is prime.

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$$(3,\gamma )$-hyperelliptic 曲线的权重边界

摘要 $(N,\gamma )$-((N,\gamma))半群是由 Fernando Torres 提出的，它概括了与（((N,\gamma))属曲线的 N 个折叠盖的完全横切点相关的 Weierstrass 半群的最显著性质。托雷斯描述了 $(2,\gamma )$-只要其属相对于 $\gamma ) 是大的，就具有最大权重的双曲半群。在这里，我们对（(3,\gamma )在这里，我们对 \((3,\gamma )$ -hyperelliptic semigroups 也做了同样的处理，并且我们对 $N \ge 3$ 是素数的一般情况提出了一个猜想。

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 Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.