Enriques和brauer类

Pub Date : 2022-02-16 DOI:10.1017/nmj.2022.43

A. Skorobogatov, D. Valloni

{"title":"Enriques和brauer类","authors":"A. Skorobogatov, D. Valloni","doi":"10.1017/nmj.2022.43","DOIUrl":null,"url":null,"abstract":"Abstract We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set \n${\\mathcal Enr}(X)$\n of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank \n$20,$\n we prove that the fibers of \n${\\mathcal Enr}(X)\\to \\mathrm {{Br}}(X)[2]$\n above the nonzero points have the same cardinality.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"ENRIQUES INVOLUTIONS AND BRAUER CLASSES\",\"authors\":\"A. Skorobogatov, D. Valloni\",\"doi\":\"10.1017/nmj.2022.43\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set \\n${\\\\mathcal Enr}(X)$\\n of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank \\n$20,$\\n we prove that the fibers of \\n${\\\\mathcal Enr}(X)\\\\to \\\\mathrm {{Br}}(X)[2]$\\n above the nonzero points have the same cardinality.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/nmj.2022.43\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2022.43","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

摘要证明了复Kummer曲面X的Brauer群中的每一个2阶元素都降为X的Enriques商。在一般情况下，给出了X的Enriques商的同构集${\数学Enr}(X)$与X的Brauer类的2阶集之间的双射。对于一些Picard秩为$20的K3曲面，我们证明了${\ mathal Enr}(X)\到$ mathal {{Br}}(X)[2]$的非零点以上的纤维具有相同的基数。

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

ENRIQUES INVOLUTIONS AND BRAUER CLASSES

Abstract We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set ${\mathcal Enr}(X)$ of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank $20,$ we prove that the fibers of ${\mathcal Enr}(X)\to \mathrm {{Br}}(X)[2]$ above the nonzero points have the same cardinality.

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