Some Cubic Surface Movies
Here are some movies (most of them were made by using the cubic
surface program). Sorry, there are not too many explanations yet, but
more of them will follow.
-
singularities.mpg:
cubic surfaces with no singularity, an A1-singularity, an A2-singularity (with lines)
-
fromCayleyToClebsch_400x400.mpg:
a walk in the space of cubic surfaces from the Cayley Cubic to the
Clebsch Diagonal Surface - with (sorry: not) all of the 27 lines
shown, too.
-
planeThroughClebsch.mpg:
How does a ranomly chosen plane cut a cubic surface?
-
planesThroughLine.mpg:
How does a plane through one of the straight lines cut a cubic surface?
-
parabolischeKurve.mpg:
A deformation of the Clebsch Diagonal Surface to a surface with two
double points. All the 27 lines and the parabolic curve are
shown. Note that each 'ellipse' of the (white) parabolic curve is
touched by three of the lines.
Now some movies created by using the Cubic Surface Program.
They are all made by moving around the point T in the plane and then
drawing the corresponding cubic surface and its tangent plane in the
point corresponding to T on the surface.
-
movingTangentPlane.mpg:
To produce the movie, we moved T somewhere around in the triangle
formed by the lines 12,36,45.
-
movingTangentPlaneOverExceptionalLine.mpg:
To produce this movie, we used the following path for T:
From T on the line 35 to the right to the point number 5, then
downwards on the line 45 until this line meets the line 12, finally
move T to the middle of the triangle 12,36,45.
-
movingTangentPlaneNotOverExceptionalLine.mpg:
To produce the movie, we used the reverse of the following path:
From T on the line 35 to the right, then downwards on the line 42,
then on the line 36 until it meets the line 12, finally move T to the
middle of the triangle 12,36,45.
Author: Oliver Labs
at the department of mathematics
of the Gutenberg University of Mainz, Germany
Home: Oliver Labs' Homepage
of the algebraic geometry group
