An invertible sheaf 𝔏 on a scheme X is called ample if for any coherent sheaf 𝔉, 𝔉𝔏n is generated by global sections for sufficiently large n.

An invertible sheaf is ample if and only if 𝔏m 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