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Concept
List of complex and algebraic surfaces
Summary
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
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