List of complex and algebraic surfaces

This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. Projective plane Cone (geometry) Cylinder Ellipsoid Hyperboloid Paraboloid Sphere Spheroid Cayley nodal cubic surface, a certain cubic surface with 4 nodes Cayley's ruled cubic surface Clebsch surface or Klein icosahedral surface Fermat cubic Monkey saddle Parabolic conoid Plücker's conoid Whitney umbrella Châtelet surfaces Dupin cyclides, inversions of a cylinder, torus, or double cone in a sphere Gabriel's horn Right circular conoid Roman surface or Steiner surface, a realization of the real projective plane in real affine space Tori, surfaces of revolution generated by a circle about a coplanar axis Boy's surface, a sextic realization of the real projective plane in real affine space Enneper surface, a nonic minimal surface Henneberg surface, a minimal surface of degree 15 Bour's minimal surface, a surface of degree 16 Richmond surfaces, a family of minimal surfaces of variable degree Coble surfaces Del Pezzo surfaces, surfaces with an ample anticanonical divisor Hirzebruch surfaces, rational ruled surfaces Segre surfaces, intersections of two quadrics in projective 4-space Unirational surfaces of characteristic 0 Veronese surface, the Veronese embedding of the projective plane into projective 5-space White surfaces, the blow-up of the projective plane at points by the linear system of degree- curves through those points Bordiga surfaces, the White surfaces determined by families of quartic curves Vanishing second Betti number: Hopf surfaces Inoue surfaces; several other families discovered by Inoue have also been called "Inoue surfaces" Positive second Betti number: Enoki surfaces Inoue–Hirzebruch surfaces Kato surfaces Kummer surfaces Tetrahedroids, special Kummer surfaces Wave surface, a special tetrahedroid Plücker surfaces, birational to Kummer surfaces Weddle surfaces, birational to Kummer surfaces Smooth quartic surfaces Super