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arXiv · 2202.08030

Enriques involutions and Brauer classes

Alexei N. Skorobogatov·Domenico Valloni
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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 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 fibres of the map from Enr(X) to Br(X)[2] above the non-zero points have the same order.

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Alexei N. Skorobogatov, Domenico Valloni. 2022-02-16. Enriques involutions and Brauer classes. https://arxiv.org/abs/2202.08030

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