With generators for $\mathcal{O}_{\mathbb{P}^n}(1)$ I mean a set $a_0,...,a_m\in \mathcal{O}_{\mathbb{P}^n}(1)(\mathbb{P}^n)$ such that $a_0,...,a_m$ generate $\mathcal{O}_{\mathbb{P}^n}(1)_P$ at all points $P$. I want to say that any generating set must have at least $n+1$ elements but I'm not sure how to prove it or if it's even true. Does anyone have an answer?
2026-03-26 23:11:10.1774566670
What is the minimal number of generators for $\mathcal{O}_{\mathbb{P}^n}(1)$?
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