{"title":"通过柯万吹胀的广义唐纳森-托马斯不变式","authors":"Jun Li, Y. Kiem, M. Savvas","doi":"10.4310/jdg/1721071499","DOIUrl":null,"url":null,"abstract":"Donaldson-Thomas (abbreviated as DT) theory is a sheaf theoretic technique of enumerating curves on a Calabi-Yau threefold. Classical DT invariants give a virtual count of Gieseker stable sheaves provided that no strictly semistable sheaves exist. This assumption was later lifted by the work of Joyce and Song who defined generalized DT invariants using Hall algebras and the Behrend function, their method being motivic in nature. In this talk, we will present a new approach towards generalized DT theory, obtaining an invariant as the degree of a virtual cycle inside a Deligne-Mumford stack. The main components are an adaptation of Kirwans partial desingularization procedure and recent results on the structure of moduli of sheaves on Calabi-Yau threefolds. Based on joint work with Young-Hoon Kiem and Jun Li. Special Note: Pre-talk at 1:30P. Host: James McKernan Friday, September 28, 2018 2:00 PM AP&M 5829 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Donaldson–Thomas invariants via Kirwan blowups\",\"authors\":\"Jun Li, Y. Kiem, M. Savvas\",\"doi\":\"10.4310/jdg/1721071499\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Donaldson-Thomas (abbreviated as DT) theory is a sheaf theoretic technique of enumerating curves on a Calabi-Yau threefold. Classical DT invariants give a virtual count of Gieseker stable sheaves provided that no strictly semistable sheaves exist. This assumption was later lifted by the work of Joyce and Song who defined generalized DT invariants using Hall algebras and the Behrend function, their method being motivic in nature. In this talk, we will present a new approach towards generalized DT theory, obtaining an invariant as the degree of a virtual cycle inside a Deligne-Mumford stack. The main components are an adaptation of Kirwans partial desingularization procedure and recent results on the structure of moduli of sheaves on Calabi-Yau threefolds. Based on joint work with Young-Hoon Kiem and Jun Li. Special Note: Pre-talk at 1:30P. Host: James McKernan Friday, September 28, 2018 2:00 PM AP&M 5829 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\",\"PeriodicalId\":15642,\"journal\":{\"name\":\"Journal of Differential Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jdg/1721071499\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jdg/1721071499","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
唐纳森-托马斯(简称 DT)理论是一种枚举 Calabi-Yau 三折上曲线的剪子理论技术。经典的 DT 变量给出了 Gieseker 稳定剪切的虚拟计数,前提是不存在严格半稳态的剪切。乔伊斯和宋后来利用霍尔代数和贝伦德函数定义了广义的 DT 变量,从本质上讲,他们的方法是动机式的。在本讲座中,我们将介绍一种实现广义 DT 理论的新方法,即通过德利尼-芒福德堆栈内部虚拟循环的度数获得不变式。其主要组成部分是对 Kirwans 部分去奇化过程的改编,以及关于 Calabi-Yau 三折上剪子的模结构的最新成果。基于与 Young-Hoon Kiem 和 Jun Li 的合作成果。特别提示:下午1:30预讲。主持人: James McKernan
Generalized Donaldson–Thomas invariants via Kirwan blowups
Donaldson-Thomas (abbreviated as DT) theory is a sheaf theoretic technique of enumerating curves on a Calabi-Yau threefold. Classical DT invariants give a virtual count of Gieseker stable sheaves provided that no strictly semistable sheaves exist. This assumption was later lifted by the work of Joyce and Song who defined generalized DT invariants using Hall algebras and the Behrend function, their method being motivic in nature. In this talk, we will present a new approach towards generalized DT theory, obtaining an invariant as the degree of a virtual cycle inside a Deligne-Mumford stack. The main components are an adaptation of Kirwans partial desingularization procedure and recent results on the structure of moduli of sheaves on Calabi-Yau threefolds. Based on joint work with Young-Hoon Kiem and Jun Li. Special Note: Pre-talk at 1:30P. Host: James McKernan Friday, September 28, 2018 2:00 PM AP&M 5829 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
期刊介绍:
Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.