加一生成曲线的加减结果

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-07-06 DOI:10.1007/s10801-024-01350-x

Anca Măcinic, Piotr Pokora

{"title":"加一生成曲线的加减结果","authors":"Anca Măcinic, Piotr Pokora","doi":"10.1007/s10801-024-01350-x","DOIUrl":null,"url":null,"abstract":"<p>In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve, the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and we derive a characterization of free curves in terms of behavior to addition/deletion of lines. Incidentally we generalize a result on conic-line arrangements by H. Schenck and Ş. Tohăneanu that describes when the addition or the deletion of a projective line from a free curve results in a free curve. We catalogue the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.\n</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"54 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Addition–deletion results for plus-one generated curves\",\"authors\":\"Anca Măcinic, Piotr Pokora\",\"doi\":\"10.1007/s10801-024-01350-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve, the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and we derive a characterization of free curves in terms of behavior to addition/deletion of lines. Incidentally we generalize a result on conic-line arrangements by H. Schenck and Ş. Tohăneanu that describes when the addition or the deletion of a projective line from a free curve results in a free curve. We catalogue the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.\\n</p>\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-06\",\"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/s10801-024-01350-x\",\"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/s10801-024-01350-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

迪姆卡（A. Dimca）在最近的论文中证明，当在自由曲线上添加或删除一条直线时，得到的曲线要么是自由的，要么是加一生成的。我们证明了相反的陈述，对最初的删除结果提出了更多的见解，并从加线/删除线的行为方面推导出自由曲线的特征。顺便提一下，我们概括了 H. Schenck 和 Ş.Tohăneanu 提出的关于圆锥曲线排列的结果，该结果描述了在自由曲线上添加或删除一条投影线时，会产生一条自由曲线。我们列出了与加一生成曲线相关的对数向量场束的可能分裂类型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Addition–deletion results for plus-one generated curves

In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve, the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and we derive a characterization of free curves in terms of behavior to addition/deletion of lines. Incidentally we generalize a result on conic-line arrangements by H. Schenck and Ş. Tohăneanu that describes when the addition or the deletion of a projective line from a free curve results in a free curve. We catalogue the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.