Effective computation of Picard groups and Brauer-Manin obstruction of   degree two K3 surfaces over number fields
  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. 
Brendan Hassett, Andrew Kresch, and Yuri Tschinkel
math.AG