Barth's sextic

Here is a a surface of degree 6 (a sextic) in projective three-space that has 65 nodes. It was discovered by W. Barth in 1996. The amazing fact here is that a sextic can never have more than 65 nodes -- so Barth's sextic is really an extreme case. It is in fact the first known example of this kind. Look into the paper to learn about the construction of the surface and its equation.

Barth's sextic

The nice computer picture shown above was made by Stephan Endrass using his program SURF. (SURF can draw pictures of a surface in three-space when you provide an equation of the surface.)

If you are interested in a classical surface, don't forget to have a look at Clebsch's diagonal cubic.

Prof. Dr. Th. Bauer   Philipps-Universität Marburg   Fachbereich Mathematik und Informatik