Dennis Borisov , Ludmil Katzarkov , Artan Sheshmani
{"title":"Shifted symplectic structures on derived Quot-stacks II – derived Quot-schemes as dg manifolds","authors":"Dennis Borisov , Ludmil Katzarkov , Artan Sheshmani","doi":"10.1016/j.aim.2024.110092","DOIUrl":null,"url":null,"abstract":"<div><div>It is proved that derived <span><math><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi></math></span>-schemes, as defined by Ciocan-Fontanine and Kapranov, are represented by dg manifolds of finite type. This is the second part of a work aimed to analyze shifted symplectic structures on moduli spaces of coherent sheaves on Calabi–Yau manifolds. The first part related dg manifolds to derived schemes as defined by Toën and Vezzosi.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"462 ","pages":"Article 110092"},"PeriodicalIF":1.5000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S000187082400608X","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
Abstract
It is proved that derived -schemes, as defined by Ciocan-Fontanine and Kapranov, are represented by dg manifolds of finite type. This is the second part of a work aimed to analyze shifted symplectic structures on moduli spaces of coherent sheaves on Calabi–Yau manifolds. The first part related dg manifolds to derived schemes as defined by Toën and Vezzosi.
期刊介绍:
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.