ample

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

An invertible sheaf is ample if and only if $\mathfrak{L}^{m}$ 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