Geometrical Animations Advent Calendar
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A Surprise
oliverlabs
5,002 views
Throughout the whole calendar we tried to show animations which explain some algebraic or geometric concept or proof.
This last one is relatively useless. It just shows...
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The Togliatti Quintic
oliverlabs
1,701 views
In this film we show how discriminants can be used to construct surfaces with many singularities. Our example will be 31-nodal quintics which is the maximum possible number...
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Polar Curves
oliverlabs
8,007 views
The polar curve PC,p from a point p to a plane curve C of degree d is a plane curve of degree d-1 which intersects the original curve C exactly in those points ti for which...
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Rational Plane Curves
oliverlabs
4,556 views
Given a curve C={f=0} of degree d in complex projective 2-space, one may ask, if C admits a parametization, i.e. if there is a rational map from projective 1-space to C wit...
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Cubic Surfaces as Blowup
oliverlabs
4,490 views
A classical result in algebraic geometry, probably first shown by A. Clebsch in the 19th century, says that any smooth complex cubic surface arises as the blowup (see no. 0...
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The Swallowtail
oliverlabs
2,460 views
Consider the univariate polynomial p(x)=x^4+ax^2+bx+c with parameters a,b,c (the cyan-colored curve in the plane which is located in the upper part of our film). It has a d...
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A Monoid with Many Singularities
oliverlabs
3,558 views
A monoid surface M is a surface of degree d with only isolated singularities and which has a singularity of multiplicity d-1. If we place this singularity at the origin O, ...
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Dual Curves
oliverlabs
11,017 views
At the left, you see a projective cubic plane curve (black), together with its tangents (white). At the right, you see its dual curve (red) which consists of those points i...
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Pinkham's Deformations
oliverlabs
1,600 views
The movie shows the projection into three-space of deformations of the cone over the rational normal curve of degree four, which is embedded in five-space. This singularity...
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Lines on Singular Cubics
oliverlabs
1,682 views
A smooth (complex) cubic surface contains exactly 27 distinct lines. On a real cubic surface, all these 27 lines can be real. When singularities occur, some of the lines fa...
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