Abstract
Let X be a real algebraic variety, we can construct another real algebraic variety by a modification of X, i.e., a sequence of blow-ups and blow-downs. In this paper, after recalling some results about the cohomology of blow-ups, we study algebraic cycles on a nonsingular real algebraic variety obtained by blow-down. Then we will consider the general case of modifications. This will allow us to prove, in particular, that the cohomology of real compact nonsingular toric varieties is algebraic.
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