On the Brauer group of Enriques surfaces

Abstract

Let S be a complex Enriques surface; it is the 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.

Minor modifications; in particular, Proposition 4.1 is put in a more general setting. v3: minor improvements in the presentation