Isolated Singularity

An isolated singularity is a Singularity for which there exists a (small) RealNumber such that there are no other Singularities within a Neighborhood ofradius centered about the Singularity.

The types of isolated singularities possible for Cubic Surfaces have been classified(Schläfli 1864, Cayley 1869, Bruce and Wall 1979) and are summarized in the following table from Fischer (1986).

Name	Symbol	Normal Form	Coxeter Diagram
conic double point
biplanar double point
biplanar double point
biplanar double point
biplanar double point
uniplanar double point
uniplanar double point
uniplanar double point
elliptic cone point	--

References

Bruce, J. and Wall, C. T. C. ``On the Classification of Cubic Surfaces.'' J. London Math. Soc. 19, 245-256, 1979.

Cayley, A. ``A Memoir on Cubic Surfaces.'' Phil. Trans. Roy. Soc. 159, 231-326, 1869.

Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, pp. 12-13, 1986.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 380-381, 1953.

Schläfli, L. ``On the Distribution of Surfaces of Third Order into Species.'' Phil. Trans. Roy. Soc. 153, 193-247, 1864.

• Pigeonhole Principle
• Pi Heptomino
• Pillai's Conjecture
• Pilot Vector
• Pinching Theorem
• Pinch Point
• Pine Cone Number
• Piriform
• Pisot-Vijayaraghavan Constants
• Pistol
• Pitchfork Bifurcation
• Pivoting
• Pivot Theorem
• Pizza Theorem
• Place (Digit)
• Place (Field)
• Place (Game)
• Planar Bubble Problem
• Planar Distance
• Planar Graph
• Planar Point
• Planar Space
• Planar Straight Line Graph
• Plancherel's Theorem
• Planck's Radiation Function