# singular set

The singular set of a variety $X$ is the set of singular points. This is a proper subvariety. A subvariety $Y$ of $X$ is contained in the singular set if and only if its local ring $\mathcal{O}_{Y}$ is not regular (http://planetmath.org/RegularLocalRing).

Title singular set SingularSet 2013-03-22 13:20:17 2013-03-22 13:20:17 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 14A15