On the Brauer Group of Real Algebraic Surfaces

dc.creatorNikulin, Viacheslav V.
dc.date1993-11-28
dc.date.accessioned2026-07-07T09:05:56Z
dc.date.available2026-07-07T09:05:56Z
dc.descriptionLet 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) \to (Z/2)^s and prove that ξis epimorphic if H^3(X(C)/G;Z/2) \to H^3(X(R);Z/2) is injective. Here G=Gal(C/R). For an algebraic surface X with H^3(X(C)/G;Z/2)=0 and X(R)\not=\emptyset, 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 s_{nor} of non-orientable components of Y which is very important for the topological classification of real Enriques surfaces.
dc.description25 pages, Ams-Tex Version 2.1
dc.identifierhttps://arxiv.org/abs/alg-geom/9311011
dc.identifierhttp://arxiv.org/abs/alg-geom/9311011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149849
dc.subjectAlgebraic Geometry
dc.titleOn the Brauer Group of Real Algebraic Surfaces
dc.typetext

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