理性表面上的幻影

IF 2.6 1区数学 Q1 MATHEMATICS

Inventiones mathematicae Pub Date : 2023-12-21 DOI:10.1007/s00222-023-01234-0

Johannes Krah

{"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":14429,"journal":{"name":"Inventiones mathematicae","volume":"3 1","pages":""},"PeriodicalIF":2.6000,"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\":14429,\"journal\":{\"name\":\"Inventiones mathematicae\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Inventiones mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00222-023-01234-0\",\"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":"Inventiones mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00222-023-01234-0","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

摘要

我们构建了一个最大长度的非全例外集合，它由 10 个一般点的投影面吹胀上的线束组成。因此，这个集合的正交补集是一个普遍幻象范畴。这为库兹涅佐夫猜想和奥洛夫猜想提供了一个反例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A phantom on a rational surface

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Inventiones mathematicae 数学-数学

CiteScore

5.60

自引率

3.20%

发文量

审稿时长

12 months

期刊介绍： This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).