Singular point of an algebraic variety (source code)

= Singular point of an algebraic variety
{wiki}

= Singular points of an algebraic variety
{synonym}

= Singular point
{synonym}

A point $p$ of an irreducible variety $X$ is singular when $\dim T_pX>\dim X$. Equivalently, its local ring is not regular. The singular locus is the complement of the smooth locus.