Enriques和brauer类

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

A. Skorobogatov, D. Valloni

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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。

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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.

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