# 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 Ample 2013-03-22 13:52:47 2013-03-22 13:52:47 archibal (4430) archibal (4430) 6 archibal (4430) Definition msc 14A99