Enriques Surfaces: Brauer groups and Kummer structures

This paper develops families of complex Enriques surfaces whose Brauer groups pull back identically to zero on the covering K3 surfaces. Our methods rely on isogenies with Kummer surfaces of product type. We offer both lattice theoretic and geometric constructions. We also sketch how the construction connects to string theory and Picard--Fuchs equations in the context of Enriques Calabi-Yau threefolds.