{"title":"$$(3,\\gamma )$-hyperelliptic 曲线的权重边界","authors":"","doi":"10.1007/s10801-023-01295-7","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p><span> <span>\\((N,\\gamma )\\)</span> </span>-<em>hyperelliptic</em> semigroups were introduced by Fernando Torres to encapsulate the most salient properties of Weierstrass semigroups associated with totally ramified points of <em>N</em>-fold covers of curves of genus <span> <span>\\(\\gamma \\)</span> </span>. Torres characterized <span> <span>\\((2,\\gamma )\\)</span> </span>-hyperelliptic semigroups of maximal weight whenever their genus is large relative to <span> <span>\\(\\gamma \\)</span> </span>. Here we do the same for <span> <span>\\((3,\\gamma )\\)</span> </span>-hyperelliptic semigroups, and we formulate a conjecture about the general case whenever <span> <span>\\(N \\ge 3\\)</span> </span> is prime.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"54 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weight bounds for $$(3,\\\\gamma )$$ -hyperelliptic curves\",\"authors\":\"\",\"doi\":\"10.1007/s10801-023-01295-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p><span> <span>\\\\((N,\\\\gamma )\\\\)</span> </span>-<em>hyperelliptic</em> semigroups were introduced by Fernando Torres to encapsulate the most salient properties of Weierstrass semigroups associated with totally ramified points of <em>N</em>-fold covers of curves of genus <span> <span>\\\\(\\\\gamma \\\\)</span> </span>. Torres characterized <span> <span>\\\\((2,\\\\gamma )\\\\)</span> </span>-hyperelliptic semigroups of maximal weight whenever their genus is large relative to <span> <span>\\\\(\\\\gamma \\\\)</span> </span>. Here we do the same for <span> <span>\\\\((3,\\\\gamma )\\\\)</span> </span>-hyperelliptic semigroups, and we formulate a conjecture about the general case whenever <span> <span>\\\\(N \\\\ge 3\\\\)</span> </span> is prime.</p>\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-023-01295-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-023-01295-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Weight bounds for $$(3,\gamma )$$ -hyperelliptic curves
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.
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.