{"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}
引用次数: 1
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
${\mathcal Enr}(X)$
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.
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