Friday, January 29, 2016

[uhmjrllh] Complex quadratic surfaces

Take the quadratic implicit equations for conic sections in 2D or quadrics in 3D and solve them over the complex numbers.  What are the shapes of the solutions?  They can no longer be plotted in Euclidean space.  We probably care about topology.

I suspect the two branches of a hyperbola will no longer be disconnected, nor will the two sheets of a hyperboloid of two sheets.

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