# ample

An invertible sheaf $\U0001d50f$ on a scheme $X$ is called *ample* if for any coherent sheaf $\U0001d509$, $\U0001d509\otimes {\U0001d50f}^{n}$ is generated by global sections for sufficiently large $n$.

An invertible sheaf is ample if and only if ${\U0001d50f}^{m}$ is very ample for some $m$; this is very often taken as the definition of ample, which can be surprising.

Title | ample |
---|---|

Canonical name | Ample |

Date of creation | 2013-03-22 13:52:47 |

Last modified on | 2013-03-22 13:52:47 |

Owner | archibal (4430) |

Last modified by | archibal (4430) |

Numerical id | 6 |

Author | archibal (4430) |

Entry type | Definition |

Classification | msc 14A99 |