Rational surface

Summary

A rational surface is an algebraic surface that is birational to the projective plane. It is the two-dimensional case of a rational variety. Rational surfaces include the projective plane, the quadric $\mathbb{P}^1 \times \mathbb{P}^1$, the Hirzebruch surfaces, the blow-ups of the plane in points, and all smooth cubic surfaces. They are the surfaces whose points can be parametrized, outside a lower-dimensional set, by two free parameters.