A characterization of dividing real algebraic curves (Q1913480)

A real nonsingular algebraic curve is called dividing if the complement of the real point set in the complexification is disconnected. The authors give characterizations of dividing curves via regular mappings to the sphere \(S^2\). For example, for a dividing curve \(X\) and any real nonsingular algebraic curve \(Y\) every regular mapping \(X\times Y\to S^2\) is null homotopic. Proofs strongly use the fact that a real curve is dividing if and only if the real point set is null homologous in the complexification of the curve.