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ENRIQUES INVOLUTIONS AND BRAUER CLASSES
Published online by Cambridge University Press: 13 December 2022
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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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
Footnotes
D.V. was funded by the European Research Council under EU Horizon 2020 research and innovation program grant agreement no. 948066.