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Nov 16, 2010 at 9:16 comment added quim These are, as Sándor points out, each (analytically) isomorphic to the vertex of a quadratic cone. See the picture here: enriques.mathematik.uni-mainz.de/docs/Ecayley.shtml I would not call them selfintersections; a selfintersecting surface would be more like Whitney's umbrella en.wikipedia.org/wiki/Whitney_umbrella where the singularity is not isolated (the surface is not normal) i.e., there are infinitely many singular points.
Nov 16, 2010 at 6:08 comment added node-question I'm referring to nodes such as the four on Cayley's cubic surface. I believe these are self-intersections of the surface, no?
Nov 16, 2010 at 5:36 history answered Sándor Kovács CC BY-SA 2.5