Friday 5 August 2011

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, some of the lines fall upon each other. E.g., on a cubic surface with three cusp singularities, 3 times 9 fall together, so that a total number of 3 distinct lines remains.

The film shows what happens when deforming this three-cuspidal surface in four different ways. The color of the lines reflects their multiplicities: orange is 9, magenta is 6, green is 3, red is 2.

More such movies can be found on our website 
http://www.cubics.algebraicsurface.net/

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