{"title":"充足的线束和生成时间","authors":"Noah Olander","doi":"10.1515/crelle-2023-0036","DOIUrl":null,"url":null,"abstract":"Abstract We prove that if X is a regular quasi-projective variety of dimension d, the set of line bundles { 𝒪 X ( n ) } n ∈ ℤ {\\{\\mathcal{O}_{X}(n)\\}_{n\\in{\\mathbb{Z}}}} generates the bounded derived category of X in d steps. This proves new cases of a conjecture of Orlov as well as a conjecture of Elagin and Lunts.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ample line bundles and generation time\",\"authors\":\"Noah Olander\",\"doi\":\"10.1515/crelle-2023-0036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove that if X is a regular quasi-projective variety of dimension d, the set of line bundles { 𝒪 X ( n ) } n ∈ ℤ {\\\\{\\\\mathcal{O}_{X}(n)\\\\}_{n\\\\in{\\\\mathbb{Z}}}} generates the bounded derived category of X in d steps. This proves new cases of a conjecture of Orlov as well as a conjecture of Elagin and Lunts.\",\"PeriodicalId\":54896,\"journal\":{\"name\":\"Journal fur die Reine und Angewandte Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal fur die Reine und Angewandte Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2023-0036\",\"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 fur die Reine und Angewandte Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/crelle-2023-0036","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract We prove that if X is a regular quasi-projective variety of dimension d, the set of line bundles { 𝒪 X ( n ) } n ∈ ℤ {\{\mathcal{O}_{X}(n)\}_{n\in{\mathbb{Z}}}} generates the bounded derived category of X in d steps. This proves new cases of a conjecture of Orlov as well as a conjecture of Elagin and Lunts.
期刊介绍：
The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.
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