Geometrie

Satz. Jede glatte kubische Fläche F entsteht durch Aufblasen von 6 Punkten in der projektiven Ebene, wobei man voraussetzen muss:


From Labs: Construct cubic surfaces as the blowup of the plane in six real points.
Programm (Labs)

The xcsprg is a tool that I was developping while I was writing my diploma thesis. Using Clebsch's representation of the cubic surface in the plane using 6 points, so that the surface is the blowup of the plane in these points, you can discover the space of cubic surfaces containing only real lines.

The screenshot below shows a typical session. In the right window, you can drag the 6 points, in the left, you see the corresponding cubic surface. Here, you see the clebsch surface, which can be represented by the 5 vertecies of a regular fivegon together with its center.