Real divisors algebraically equivalent to zero

Abstract

defined on the group Z k (X) of algebraic cycles on X of codimension k:for any closed subvariety V of X of codimension k, the cohomology class cR(V )i s Poincare dual to the homology class in Hn−k(X(R), Z/2) represented by V (R )i f dim V (R )= n − k (cf. (4) or (2, Section 11.3) for the definition of this homology class) and cR(V )=0i f dimV (R) <n − k. Of fundamental interest in real algebraic geometry is the image H k alg (X(R), Z/2) = cR(Z k (X)) of Z k (X) via cR (cf. (3) for a short survey of its properties and applications). Recently also the subgroup Alg k (X(R)) = cR(Z k (X)) of H k (X(R), Z/2), where Z k alg (X) is the subgroup of Z k (X) consisting of all