On Brauer groups of real Enriques surfaces

Abstract

Let Y be a real Enriques surface, ₂Br(Y ) the subgroup of elements of order 2 of Br(Y ), and s, s_or, and s_nor the number of all connected, connected orientable, and connected non-orientable components of Y (R) respectively. Using universal covering K3-surface X of Y , we connect dim₂ Br(Y ) with s, s_or and s_nor. As a geometric corollary of our considerations, we show that s ≤ 6 and s_nor ≤ 4.