On the Brauer group of Enriques surfaces

Let $S$ be a complex Enriques surface (quotient of a K3 surface $X$ by a fixed-point-free involution). The Brauer group $\Br(S)$ has a unique nonzero element. We describe its pull-back in $\Br(X)$, and show that the surfaces $S$ for which it is trivial form a countable union of hypersurfaces in the moduli space of Enriques surfaces.

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Published 1 January 2009