1993/11/28 by Viacheslav V. Nikulin, Nikulin, Viacheslav V.
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.alg-geom/9311011
openalex publication_date 1993/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a real projective algebraic manifold, s numerates connected components of X(R) and 2Br(X) the subgroup of elements of order 2 of the cohomological Brauer group Br(X). We study the natural homomorphism ξ: 2Br(X) → (Z/2)s and prove that ξis epimorphic if H3(X(C)/G;Z/2) → H3(X(R);Z/2) is injective. Here G=Gal(C/R). For an algebraic surface X with H3(X(C)/G;Z/2)=0 and X(R)\not=∅, we give a formula for dim 2Br(X). As a corollary, for a real Enriques surfaces Y, the ξis epimorphic and dim 2Br(Y)=2s-1 if both liftings of the antiholomorphic involution of Y to the universal covering K3- surface X have non-empty sets of real points (this is the general case). For this case, we also give a formula for the number snor of non-orientable components of Y which is very important for the topological classification of real Enriques surfaces.