A real algebraic curve in projective \(n\)-space is called unramified if the degree of any divisor cut out by a real hyperplane overcomes the number of points in the divisor by at most \(n-1\) (here a pair of imaginary conjugate points is thought of as one point). Over the complex field, the unramified curves are known to be rational normal. Real plane unramified curves are conics [J. Huisman, An unramified real plane curve is a conic, Matematiche 55, 459–467 (2000); http://fraise.univ-brest.fr/~huisman/recherche/publications.html].
In the present note, the author shows that a real plane unramified nonspecial curve in an even-dimensional space is rational normal, and in an odd-dimensional space he shows that it is an \(M\)-curve consisting of pseudo-lines, provided that the curve under consideration has many real branches and, possibly, few ovals. The proof is based on the study of coverings of the real part of the Picard variety by unions of real branches of a curve.