{"title":"理性表面上的幻影","authors":"Johannes Krah","doi":"10.1007/s00222-023-01234-0","DOIUrl":null,"url":null,"abstract":"<p>We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A phantom on a rational surface\",\"authors\":\"Johannes Krah\",\"doi\":\"10.1007/s00222-023-01234-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00222-023-01234-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00222-023-01234-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
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