K3 fibrations on rigid double octic Calabi–Yau threefolds
Volume 116 / 2016
Annales Polonici Mathematici 116 (2016), 229-241
MSC: Primary 14J32; Secondary 14D06.
DOI: 10.4064/ap3872-4-2016
Published online: 18 May 2016
Abstract
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.
