K3 fibrations on rigid double octic Calabi-Yau threefolds
We give a description of the Picard group of double octic Calabi-Yau threefolds using a K3 fibration defined by a singular line of the branch octic. In particular, we show that the group is generated by the Picard group of a generic fibre and the subgroup generated by the components of the reducible fibres.