# normal variety

Let $X$ be a variety^{}. $X$ is said to be normal at a point $p\in X$ if the local ring^{} ${\mathcal{O}}_{p}$ is integrally closed^{}. $X$ is said to be normal if it is normal at every point. If $X$ is non-singular^{} at $p$, it is normal at $p$, since regular local rings^{} are integrally closed.

Title | normal variety |
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Canonical name | NormalVariety |

Date of creation | 2013-03-22 13:20:28 |

Last modified on | 2013-03-22 13:20:28 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 5 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 14M05 |