Rational Double Points

Introduction
The Gallery
The Rational Double Points
Rational Double Points Other Singularities Tools Bibliography                  

The Cubic Surfaces with Only Rational Double Points

Schl?fli already classified all real cubic surfaces with respect to the singularities occurring on them in 1863. Kn?rrer/Miller gave a more rigorous classification in 1987.

In this section, we give equations and images for all of their 45 types which only have rational double points as singularities. The example on the left has one A1 and one A5 singularity.

In our gallery the lines on the cubic surfaces are colored according to their multiplicity.
This is particularly interesting when looking at an animation which shows the deformation of one type of cubic surfaces into another (see e.g. the deformations of the four-nodal Cayley cubic).

>>> Go to the gallery!