The Brauer-Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface

摘要

This paper discusses the Brauer-Manin obstruction on double covers of the projective plane branched along a plane section of a Kummer surface from both the practical and the theoretical points of view. Theoretical highlights include the determination of a complete set of generators for the Brauer group; on the practical side, we give several surfaces with a Brauer-Manin obstruction and verify that the Brauer-Manin obstruction is the only one for a collection of several thousand surfaces of this type.