环状排列紧凑模型的同调基础

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-03-26 DOI:10.4310/pamq.2024.v20.n1.a9

Giovanni Gaiffi, Oscar Papini

{"title":"环状排列紧凑模型的同调基础","authors":"Giovanni Gaiffi, Oscar Papini","doi":"10.4310/pamq.2024.v20.n1.a9","DOIUrl":null,"url":null,"abstract":"In this paper we find monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. We provide some examples computed via a SageMath program and then we focus on the case of the toric arrangements associated with root systems of type $A$. Here the combinatorial description of our basis offers a geometrical point of view on the relation between some Eulerian statistics on the symmetric group.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"44 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A basis for the cohomology of compact models of toric arrangements\",\"authors\":\"Giovanni Gaiffi, Oscar Papini\",\"doi\":\"10.4310/pamq.2024.v20.n1.a9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we find monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. We provide some examples computed via a SageMath program and then we focus on the case of the toric arrangements associated with root systems of type $A$. Here the combinatorial description of our basis offers a geometrical point of view on the relation between some Eulerian statistics on the symmetric group.\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2024.v20.n1.a9\",\"RegionNum\":4,\"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":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n1.a9","RegionNum":4,"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

在本文中，我们找到了环状排列的紧凑奇妙模型的整数同调环的单项式基。在单项式的描述中，各种组合对象都会发挥作用：构建集、嵌套集和合适的环状变的扇形。我们提供了一些通过 SageMath 程序计算的示例，然后重点讨论了与 $A$ 类型根系统相关的环状排列的情况。在这里，我们对基础的组合描述为对称群上一些欧拉统计量之间的关系提供了一个几何视角。

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

A basis for the cohomology of compact models of toric arrangements

In this paper we find monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. We provide some examples computed via a SageMath program and then we focus on the case of the toric arrangements associated with root systems of type $A$. Here the combinatorial description of our basis offers a geometrical point of view on the relation between some Eulerian statistics on the symmetric group.

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

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.