How can we describe $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1}(m))$ as a gluing of affine charts? I'm having trouble with this problem, perhaps because I don't understand the geometry of what's going on particularly well. I'm also meant to do the same for $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1}(-m))$. Is anyone willing to walk me through it?
2026-03-29 11:44:36.1774784676
Describing $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1}(m))$ as gluing of affine charts
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