Talk:Blowing up

I just did a &quot;major reorganization and expansion&quot;, 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 &quot;exceptional&quot; 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 &quot;birational map&quot; should really be defined).

I started all of this because someone requested an article on &quot;Exceptional divisor&quot;. 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?
I'm talking about 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)

Proposed merge of Blowing down into this article
Yes, Blowing down should be merged into this article. Blowing down has existed since 2005 and still has very little content. Merging it into Blowing up was proposed as early as 2007. Mgnbar (talk) 13:06, 22 March 2018 (UTC)

Possible mistake
"By projective duality, G(1,2) is isomorphic to P2". Is it? I think that G(1,2) is the projective line, not the projective plane. AndreaGMonaco (talk) 16:10, 19 May 2022 (UTC)

{Z} instead of just Z (the point) twice in the section "Blowing up points in complex space"
I think in two places in this sections there should be curly brackets around the point Z to indicate that it's the set with point Z. AndreasMath (talk) 12:13, 27 March 2024 (UTC)


 * At that point in the article, only isolated points have been blown up. So I don't think that the distinction between a point and a one-point set is helpful or necessary. If you want to connect one-point blow ups to the later sections, then you might add a note at the end of the section or the beginning of a later section, saying that the one-point case is {Z}.
 * Really, this article has much bigger issues of presentation. For example, the first section should present the concrete, coordinate-based description long before mentioning the Grassmannian. Once the article has been rewritten for better presentation, then we can debate and polish these smaller considerations. That is my opinion. Regards, Mgnbar (talk) 12:49, 27 March 2024 (UTC)
 * I certainly agree that it's no big issue and I've only referred to the two uses in the mathematical expressions. Where it mixes inconsistently the point Z with set operations: $$E = Z \times \mathbf{P}^{n - 1} \subseteq \mathbf{C}^n \times \mathbf{P}^{n - 1}$$ and Cn \ Z.
 * Just thought it is more of a typo or a small thing that has been overlooked since later it correctly says $$ \lbrace Z\rbrace\times\mathbf{P}^{n-1}$$. And since I am not actively working on this article I don't want to edit others work. Best, AndreasMath (talk) 13:31, 27 March 2024 (UTC)