On the computation of the Picard group for K3 surfaces

Titelangaben

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
On the computation of the Picard group for K3 surfaces.
In: Mathematical Proceedings of the Cambridge Philosophical Society. Bd. 151 (2011) Heft 2 . - S. 263-270.
ISSN 0305-0041
DOI: https://doi.org/10.1017/S0305004111000326

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Abstract

We present a method to construct examples of K3 surfaces of geometric Picard rank 1. Our approach is a refinement of that of R. van Luijk. It is based on an analysis of the
Galois module structure on étale cohomology. This allows us to abandon the original limitation to cases of Picard rank 2 after reduction modulo p. Furthermore, the use of Galois data enables us to construct examples that require significantly less computation time.