2022/02/16 by Alexei N. Skorobogatov, Skorobogatov, Alexei N., Domenico Valloni +1
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2202.08030
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.