II.4.3

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This has H = 3, V = ....

HAPPY

• Show $U \cap V \cong \Delta(X) \cap (U \times V)$
• technically II.3.13b can used to conclude $\Delta(X) \cap (U \times V)$ is affine, but (I think) Cor. II.5.10 is a better way to prove II.3.13b.
• For a counterexample when $X$ is not separated glue to copies of $\mathbb{A}^2$ along $\mathbb{A}^2 - (0,0)$.
• this example lets you use ex I.3.6.