An isolated singularity is a singularity for which there exists a (small) real number 
such that there are no other singularities
within a neighborhood of radius 
centered about the singularity.
Isolated singularities are also known as conic double points.
The types of isolated singularities possible for cubic surfaces have been classified (Schläfli 1863, Cayley 1869, Bruce and Wall 1979) and are summarized in the following table from Fischer (1986).
See also
Cubic Surface, Rational Double Point, Singular Point
Explore with Wolfram|Alpha
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.). Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband. Braunschweig, Germany: Vieweg, pp. 12-13, 1986.Krantz, S. G. Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 41, 1999.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, in Reference to the Absence or Presence of Singular Points, and the Reality of Their Lines." Philos. Trans. Roy. Soc. London 153, 193-241, 1863.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Isolated Singularity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IsolatedSingularity.html