# 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 |
---|---|

Canonical name | SingularSet |

Date of creation | 2013-03-22 13:20:17 |

Last modified on | 2013-03-22 13:20:17 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 14A15 |