II.4.3

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.