Let k be a number field. We give an explicit bound, depending only on [k: Q], on the size of the Brauer group of a K3 surface X/k that is geometrically isomorphic to the Kummer surface attached to a product of CM elliptic curves. As an application, we show that the Brauer–Manin set for such a variety is effectively computable. In addition, we prove an effective version of the strong Shafarevich conjecture for singular K3 surfaces by giving an explicit bound, depending only on [k: Q], on the number of C-isomorphism classes of singular K3 surfaces defined over k.
MSC Codes 14F22 (Primary) 14J28, 14G05 (Secondary)
|Original language||English (US)|
|State||Published - Jun 26 2020|