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An algebraic surface is defined as the set of points

that satisfy a polynomial equation

. An ordinary double point (or node) is a point where the surface intersects itself and satisfies

. The maximum possible number of nodes is a function of the degree of

References

[1] S. Endrass. "Surf: Visualizing Real Algebraic Geometry." (Sep 17, 2013) www2.mathematik.uni-mainz.de/alggeom/surf/links.shtml.

[2] O. Labs. "AlgebraicSurface.net." (Sep 17, 2013) www.algebraicsurface.net.

[3] Mathematisches Forschungsinstitut Oberwolfach. "IMAGINARY—Open Mathematics." (Sep 17, 2013) imaginary.org.

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Algebraic Surfaces with Many Nodes