{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":"116 12","pages":""},"PeriodicalIF":16.4000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jdg/1721071499","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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.