Enriques和brauer类

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal 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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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.