Effective computation of Picard groups and Brauer-Manin obstruction of degree two K3 surfaces over number fields

TL;DR

This paper presents an effective algorithm leveraging the Kuga-Satake correspondence to compute the Picard and Brauer groups of degree two K3 surfaces over number fields, aiding in understanding their arithmetic properties.

Contribution

It introduces a novel, effective computational method for Picard and Brauer groups of degree two K3 surfaces using the Kuga-Satake correspondence.

Findings

Algorithm successfully computes Picard groups.

Algorithm effectively determines Brauer groups.

Enhances understanding of K3 surface arithmetic.

Abstract

Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.