{"title":"Recursion Formulas on Hall Numbers for Weighted Projective Lines","authors":"Xiaofeng Zhang","doi":"10.1007/s11464-021-0123-6","DOIUrl":null,"url":null,"abstract":"We study the property of Hall numbers for the category of coherent sheaves over a weighted projective line. Several recursion formulas on Hall numbers are obtained, whose proofs rely on Green’s formula. Similar formulas for tame quivers and cyclic quivers are discussed.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"57 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers of Mathematics in China","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11464-021-0123-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the property of Hall numbers for the category of coherent sheaves over a weighted projective line. Several recursion formulas on Hall numbers are obtained, whose proofs rely on Green’s formula. Similar formulas for tame quivers and cyclic quivers are discussed.
期刊介绍：
Frontiers of Mathematics in China provides a forum for a broad blend of peer-reviewed scholarly papers in order to promote rapid communication of mathematical developments. It reflects the enormous advances that are currently being made in the field of mathematics. The subject areas featured include all main branches of mathematics, both pure and applied. In addition to core areas (such as geometry, algebra, topology, number theory, real and complex function theory, functional analysis, probability theory, combinatorics and graph theory, dynamical systems and differential equations), applied areas (such as statistics, computational mathematics, numerical analysis, mathematical biology, mathematical finance and the like) will also be selected. The journal especially encourages papers in developing and promising fields as well as papers showing the interaction between different areas of mathematics, or the interaction between mathematics and science and engineering.
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