Examples of Rational Surfaces
- Bordiga surfaces: A degree 6 embedding of the projective plane into P4 defined by the quartics through 10 points in general position.
- Châtelet surfaces
- Coble surfaces
- Cubic surfaces Nonsingular cubic surfaces are isomorphic to the projective plane blown up in 6 points, and are Fano surfaces. Named examples include the Fermat cubic, the Cayley cubic surface, and the Clebsch diagonal surface.
- del Pezzo surfaces (Fano surfaces)
- Enneper surface
- Hirzebruch surfaces Σn
- P1×P1 The product of two projective lines is the Hirzebruch surface Σ0. It is the only surface with two different rulings.
- The projective plane
- Segre surface An intersection of two quadrics, isomorphic to the projective plane blown up in 5 points.
- Steiner surface A surface in P4 with singularities which is birational to the projective plane.
- White surfaces, a generalization of Bordiga surfaces.
- Veronese surface An embedding of the projective plane into P5.
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