Generalized Donaldson–Thomas invariants via Kirwan blowups

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Jun Li, Y. Kiem, M. Savvas
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引用次数: 0

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 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
通过柯万吹胀的广义唐纳森-托马斯不变式
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
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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