On the Brauer group of Enriques surfaces

Mathematics – Algebraic Geometry

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

Scientific paper

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.

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