On the computation of the Picard group for $K3$ surfaces
Algebraic Geometry
2015-05-19 v1
Abstract
We construct examples of surfaces of geometric Picard rank . Our method is a refinement of that of R. van Luijk. It is based on an analysis of the Galois module structure on \'etale cohomology. This allows to abandon the original limitation to cases of Picard rank after reduction modulo . Furthermore, the use of Galois data enables us to construct examples which require significantly less computation time.
Cite
@article{arxiv.1006.1724,
title = {On the computation of the Picard group for $K3$ surfaces},
author = {Andreas-Stephan Elsenhans and Jörg Jahnel},
journal= {arXiv preprint arXiv:1006.1724},
year = {2015}
}