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oliverlabs

A Surprise
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...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:34
Rating: 3.9
Views: 5021
 
Tags: advent  calendar  geometry  algebraic  oliverlabs  
 
Pinkham's Deformations
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....
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:37
Rating: 5.0
Views: 1621
 
Tags: advent  calendar  geometry  algebraic  oliverlabs  
 
Cubic Surfaces as Blowup
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...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:48
Rating: 4.5
Views: 4604
 
Tags: advent  calendar  geometry  algebraic  mathematics  oliverlabs  
 
Blowup in a Point
Today, we present the standard picture which appears in any algebraic geometry text book in the form of an animation: the blowup of the affine...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:37
Rating: 4.8333335
Views: 6335
 
Tags: advent  calendar  geometry  algebraic  mathematics  oliverlabs  
 
The Hessian
The hessian of a hypersurface is the determinant of the matrix of its second partial derivatives. The hessian of a plane curve intersects the curve...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 01:13
Rating: 4.2222223
Views: 17261
 
Tags: advent  calendar  geometry  algebraic  mathematics  oliverlabs  
 
Dual Curves
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)...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:44
Rating: 3.764706
Views: 11099
 
Tags: advent  calendar  geometry  algebraic  mathematics  oliverlabs  
 
Lines on Singular Cubics
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,...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:22
Rating: 5.0
Views: 1713
 
Tags: advent  calendar  geometry  algebraic  oliverlabs  
 
Vanishing Cycles
The movie shows a generic deformation of the A4-Singularity. One can clearly see the chain consisting of four cycles that is contracted in the singularity:...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:36
Rating: 3.2222223
Views: 4030
 
Tags: advent  calendar  geometry  algebraic  mathematics  oliverlabs  
 
The Togliatti Quintic
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...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 01:13
Rating: 5.0
Views: 1719
 
Tags: advent  calendar  geometry  algebraic  oliverlabs  
 
Polar Curves
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...
 
Uploaded: December 31, 1969 at 4:59 pm
Author: oliverlabs
 
Length: 00:43
Rating: 4.4166665
Views: 8162
 
Tags: advent  calendar  geometry  algebraic  oliverlabs  
 


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