Enriques Surfaces: Brauer Groups and Kummer Structures

摘要

The Brauer group is an important but very subtle birational invariant of a pro-jective surface. In [3], Beauville proved that generically the Brauer group of a complex Enriques surface injects into the Brauer group of the covering K3 surface. Subsequently Beauville asked for explicit examples where the Brauer groups pull back identically to zero. This problem has recently been solved in [6] (see also Section 7.10) and in [7], but only by isolated so-called singular K3 surfaces (Picard number 20). In this paper we develop methods to derive such surfaces in 1-dimensional families.