= Ideal sheaf of two closed points
{title2=$\mathcal I_{\{P,Q\}}=\mathcal I_P\cap\mathcal I_Q$}
For distinct <closed points> over an <algebraically closed field>, evaluation gives the <short exact sequence> $0\to\mathcal I_{\{P,Q\}}\to\mathcal O_X\to k_P\oplus k_Q\to0$. If all global <regular functions> are constant, the <long exact sequence in sheaf cohomology> embeds $k^2/k(1,1)$ into $H^1(X,\mathcal I_{\{P,Q\}})$. Thus this ideal detects a concrete obstruction to affineness.
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