Talk:Blowing up

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated C-class, Mid-priority)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
C Class
Mid Priority
 Field:  Geometry

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 and 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

Just wondering, Blowing up can also refer to the act of exploding something - does anyone else agree that this is a disambiguation or at least worthy of a link? --Pcmattman (talk) 10:14, 15 May 2008 (UTC)

You're right; there should be a disambiguation link to Explosion, say. But I think that there should not be a whole disambiguation page. Joshua R. Davis (talk) 12:42, 15 May 2008 (UTC)
I added an otheruses template to the start of the page to clarify this disambiguation. --Pcmattman (talk) 04:00, 18 May 2008 (UTC)

Relation to blow-up in PDEs?[edit]

I'm talking about [1] Is there one? — Preceding unsigned comment added by 86.127.138.234 (talk) 22:29, 28 January 2015 (UTC)

No. That kind of blowup is when a solution of a differential equation becomes unbounded in finite time. The kind of blowup in the present article is a way of zooming in more closely at a point to see fine structure. Ozob (talk) 03:26, 29 January 2015 (UTC)