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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.

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