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Sep 17, 2011 at 15:30 comment added Ying Zhang Nice. Looking back at this example, the strict transform of a nice $P^1$ is "strict" on the top since it passes through one of the points we blow up. It is a nice exercise to write down the total transform and see it on the nose that pulling back keeps the self-intersection number 0.
Sep 16, 2011 at 1:52 history answered Allen Knutson CC BY-SA 3.0