# List of complex and algebraic surfaces

This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to the Enriques–Kodaira classification.

## Kodaira dimension ${\displaystyle 0}$

### Enriques surfaces

• Reye congruences, the locus of lines that lie on two out of three general quadric surfaces in projective space

### Abelian surfaces

• Horrocks–Mumford surfaces, surfaces of degree 10 in projective 4-space that are the zero locus of sections of the rank-two Horrocks–Mumford bundle

## Families of surfaces with members in multiple classes

• Surfaces that are also Shimura varieties:
• Elliptic surfaces, surfaces with an elliptic fibration; quasielliptic surfaces constitute a modification this idea that occurs in finite characteristic
• Exceptional surfaces, surfaces whose Picard number achieve the bound set by the central Hodge number h1,1
• Kähler surfaces, complex surfaces with a Kähler metric; equivalently, surfaces for which the first Betti number b1 is even
• Minimal surfaces, surfaces that can't be obtained from another by blowing up at a point; they have no connection with the minimal surfaces of differential geometry
• Nodal surfaces, surfaces whose only singularities are nodes
• Cayley's nodal cubic, which has 4 nodes
• Kummer surfaces, quartic surfaces with 16 nodes
• Togliatti surface, a certain quintic with 31 nodes
• Barth surfaces, referring to a certain sextic with 65 nodes and decic with 345 nodes
• Labs surface, a certain septic with 99 nodes
• Endrass surface, a certain surface of degree 8 with 168 nodes
• Sarti surface, a certain surface of degree 12 with 600 nodes
• Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces
• Zariski surfaces, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane