二次曲面束的残馀范畴

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-03-02 DOI:10.1515/crelle-2022-0092

F. Xie

{"title":"二次曲面束的残馀范畴","authors":"F. Xie","doi":"10.1515/crelle-2022-0092","DOIUrl":null,"url":null,"abstract":"Abstract We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. • Case 1: The quadric surface bundle has a smooth section. • Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":"185 1","pages":"161 - 199"},"PeriodicalIF":1.2000,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Residual categories of quadric surface bundles\",\"authors\":\"F. Xie\",\"doi\":\"10.1515/crelle-2022-0092\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. • Case 1: The quadric surface bundle has a smooth section. • Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.\",\"PeriodicalId\":54896,\"journal\":{\"name\":\"Journal fur die Reine und Angewandte Mathematik\",\"volume\":\"185 1\",\"pages\":\"161 - 199\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-03-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal fur die Reine und Angewandte Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2022-0092\",\"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-2022-0092","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: 1

摘要

摘要在下列假设下，证明了二次曲面束的残差范畴等价于某些格式的(扭曲)派生范畴。案例1:二次曲面束具有光滑截面。•情况2:二次曲面束的总空间是光滑的，并且基座是光滑的表面。在情形1中，我们提供了两个证明，分别将该格式描述为双曲化简和相对希尔伯特格式的子格式。在情形2中，扭曲格式是通过对直线的相对希尔伯特格式进行双态变换得到的。最后，将所得结果应用于二次曲面的完全交点。

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

Residual categories of quadric surface bundles

Abstract We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. • Case 1: The quadric surface bundle has a smooth section. • Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.

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

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

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.