An invariance property of algebraic curves inP ² (R)

Abstract

In a sequel to [2] the authors study algebraic curves in |R² which are mapped into themselves by the reflection-inversionS(y):=−||y||⁻² y(y(yɛ|R²{(0,0)}), a birational transformation of the plane. It is shown that every curve with this property is, essentially, the combined image of two homeomorphic models of a real projective algebraic curve in the standard model ofp ²(|R). Curves of low degree possessing this property are then identified.