Some Named Algebraic Surfaces
An algebraic surface can be defined as the set of points that are the zeros of a polynomial . This Demonstration plots a collection of named algebraic surfaces with different types of singularities. You can adjust the precision Mathematica uses to estimate the zeros (recursion), as well as the shape (region) and size (range) of the region in which the zeros are plotted.
The examples in this Demonstration are taken from the gallery of Herwig Hauser .
 H. Hauser. "Algebraic Surfaces Gallery." (Sept 6, 2013) homepage.univie.ac.at/herwig.hauser/gallery.html.