Real algebraic curves and complete intersections
This paper is devoted to the proof of a special result of complete intersections for real algebraic curves when the curve is contained in an admissible (technical definition in the first page of the paper) real algebraic variety. It applies in particular to the case of affine or projective space and to n-dimensional spheres. This kind of result is not true in the algebraically closed case. The technique of the proof is the following: - prove a lemma of \(C^{\infty}\) complete intersections; - use the resolution of singularities and the theory of strongly algebraic vector bundles which gives in some special cases the fact that \(C^{\infty}\) real line bundles can be represented by strongly algebraic vector bundles.
complete intersections for real algebraic curves
scientific article; zbMATH DE number 4087821