Spectrum map for the complexification of a real polynomial ring ($\mathrm{Spec}\mathbb{C}[x]\to \mathrm{Spec}\mathbb{R}[x]$)

Contraction sends the zero prime ideal to zero. A complex closed point $(x-z)$ contracts to $(x-z)$ when $z$ is real, and to $((x-\mathrm{Re}z{)}^2+(\mathrm{Im}z{)}^2)$ otherwise. Thus the map on the spectrum of a commutative ring is surjective and identifies each nonreal conjugate pair. Both spectra have only finite proper Zariski-closed sets, so this is also the topological quotient by complex conjugation.