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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3872-4-2016,
author = {Pawe\l\ Bor\'owka},
title = {K3 fibrations on rigid double octic Calabi-Yau threefolds},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {229-241},
zbl = {06586884},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3872-4-2016}
}
Paweł Borówka. K3 fibrations on rigid double octic Calabi-Yau threefolds. Annales Polonici Mathematici, Tome 116 (2016) pp. 229-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3872-4-2016/