{"title":"hard - narasimhan过滤和之字形持久性","authors":"Marc Fersztand, Vidit Nanda, Ulrike Tillmann","doi":"10.1016/j.aam.2023.102634","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.</p></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0196885823001525/pdfft?md5=07718e8ee4d02f79c22f258585733bd9&pid=1-s2.0-S0196885823001525-main.pdf","citationCount":"1","resultStr":"{\"title\":\"Harder-Narasimhan filtrations and zigzag persistence\",\"authors\":\"Marc Fersztand, Vidit Nanda, Ulrike Tillmann\",\"doi\":\"10.1016/j.aam.2023.102634\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.</p></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0196885823001525/pdfft?md5=07718e8ee4d02f79c22f258585733bd9&pid=1-s2.0-S0196885823001525-main.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0196885823001525\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885823001525","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Harder-Narasimhan filtrations and zigzag persistence
We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.
期刊介绍：
Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas.
Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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