Talk:Blowing up

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You have new messages (last change).

I just did a "major reorganization and expansion", so I apologize for stepping on toes. I'm being bold.

I'm most comfortable with blow-ups in the smooth complex category, so somebody with broader knowledge could probably connect the scheme-theoretic part better to the rest of the article. In particular, I'm not sure what conditions on X and V are needed for deformation to the normal cone.

I claim that the exceptional divisor is "exceptional" because it's isolated; but perhaps it's exceptional because it's not in the domain of the birational map? I don't really know.

I think I've heard that any birational map factors as a sequence of blow-ups and blow-downs. That's worth mentioning (perhaps in Birational geometry, where "birational map" should really be defined).

I started all of this because someone requested an article on "Exceptional divisor". However, it is only referenced in the Cubic surface article, so I think I'll connect that link to here instead. Joshuardavis

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