Nodal surface
In algebraic geometry, a nodal surface is a surface in projective space whose only singularities are nodes. A major problem about them is to find the maximum number of nodes of a nodal surface of given degree.
The following table gives some known upper and lower bounds for the maximal number of nodes on a complex surface of given degree.
| Degree | Lower bound | Surface achieving lower bound | Upper bound |
| 1 | 0 | Plane | 0 |
| 2 | 1 | Conical surface | 1 |
| 3 | 4 | Cayley's nodal cubic surface | 4 |
| 4 | 16 | Kummer surface | 16 |
| 5 | 31 | Togliatti surface | 31 |
| 6 | 65 | Barth sextic | 65 |
| 7 | 99 | Labs septic | 104 |
| 8 | 168 | Endraß surface | 174 |
| 9 | 226 | Labs | 246 |
| 10 | 345 | Barth decic | 360 |
| 11 | 425 | 480 | |
| 12 | 600 | Sarti surface | 645 |
| d | d | d2 |