A singular variety is an algebraic variety having at least one singular point. Equivalently, it is a variety that is not smooth everywhere. The set of its singular points is its singular locus, the complement of the smooth locus.
Singular Variety
See also
Singular Point, Smooth Locus, Smooth VarietyExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Singular Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SingularVariety.html