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Abstract: We show that every affine or projective algebraic variety defined over R or C is homeomorphic to a variety defined over the field of algebraic numbers. We construct such homeomorphism by choosing a small deformation of the coefficients of the original equations. This method is based on the properties of Zariski equisingular families of varieties. (Based on a joint paper with Guillaume Rond.) A similar local result for analytic function germs was obtained by Guillaume Rond.
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