On the Picard number of K3 surfaces over number fields
Algebraic Geometry
2011-11-18 v1
Abstract
We discuss some aspects of the behavior of specialization at a finite place of N\'eron-Severi groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard number of such specializations, thus answering a question of Elsenhans and Jahnel. As a consequence of these results, we show that it is possible to explicitly compute the Picard number of any given K3 surface over a number field.
Cite
@article{arxiv.1111.4117,
title = {On the Picard number of K3 surfaces over number fields},
author = {François Charles},
journal= {arXiv preprint arXiv:1111.4117},
year = {2011}
}
Comments
14 pages, comments welcome