Globally generated line bundle without finite generators
= Globally generated line bundle without finite generators
{title2=$X=\coprod_{m\geq1}\mathbb P^m,\quad\mathcal L|_{\mathbb P^m}=\mathcal O(1)$}
The displayed line bundle is globally generated, but no finite family of <global sections> generates it. A family of $N$ sections restricts to $N$ linear forms on $\mathbb P^m$; for $m\geq N$, these have a common zero. This shows why <finite global generation on a quasi-compact scheme> requires its finiteness hypothesis.