Testwiki:Articles for deletion/Smooth completion

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep. Possible renaming can be considered as part of normal editing. JohnCD (talk) 11:04, 13 February 2012 (UTC)

Smooth completion

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This article is better suited for Wiktionary Wikishagnik (talk) 17:32, 4 February 2012 (UTC)

Note: This debate has been included in the list of Science-related deletion discussions. • Gene93k (talk) 17:44, 4 February 2012 (UTC)

• delete: "Smooth completion" is a non sourced terminology, which contradicts the usual mathematical meaning of "completion", which supposes that the completed space is embedded in its completion (this is not the case here). Moreover, this terminology is not notable, the usual one being "normalization of the projective completion" or "desingularization of the projective completion". D.Lazard (talk) 18:29, 4 February 2012 (UTC)

This appears to be a mathematical error on D.Lazard's part. If the affine curve is nonsingular, then it is indeed imbedded in the smooth completion. Tkuvho (talk) 19:30, 4 February 2012 (UTC)

Understood your logic but the article still belongs to Wiktionary Wikishagnik (talk) 20:15, 4 February 2012 (UTC)

I think your comment is based on the assumption that the current form of the stub is its current form. You may have noticed, however, that the article was only created a short while ago, and has not received the attention it deserves. The "wiktionary" idea does not apply to it more than any other math article in wikipedia. Tkuvho (talk) 20:17, 4 February 2012 (UTC)

Short While Ago? The Article was created on 5th Jan 2012?Wikishagnik (talk) 20:52, 4 February 2012 (UTC)

• Move to Smooth compactification: It seems like the term "smooth completion" is used (from a quick google scholar search), but I've never heard it. On the other hand, "smooth compactification" is a quite common term for what seems to be the subject of this article (and it applies to varieties of higher dimension) and it a quite notable subject. I disagree with the statement that this belongs on wiktionary for the same reason Tkuvho mentions above: the same would hold for plently of other math articles (especially stubs). RobHar (talk) 20:32, 4 February 2012 (UTC)

I agree that the "compactification" title is more logical, but I happened to have heard "smooth completion" in this context. I guess the thing to do is to look at reliable sources. What would this be called in a standard textbook? Tkuvho (talk) 20:49, 4 February 2012 (UTC)

• Keep (although have not objections against renaming), it is a quite common subject in complex geometry.

  Sadly, there are many Wikipedians which basically misunderstand the purpose of Wiktionary and think about it as about "unWikipedia for very short articles". But the difference is actually in the subject, not size. Wikipedia should describe pieces of knowledge represented by words. Wiktionary is for knowledge about words, which obviously is not this case. Incnis Mrsi (talk) 20:39, 4 February 2012 (UTC)

I think this confusion will exist till the time people think of Wiktionary to be an inferior cousin of Wikipedia. Agreed that people and experts spend more time on Wikipedia but that does not mean we create pages for every documented variation of a mathematical formula. Wiktionary is better suited to understand a concept while Wikipedia is better suited for giving it a historical context, contribution to humanity. I know that a lot of people try to use Wikipedia as a textbook on scientific topics but that defeats the whole purpose of an encyclopedia. We cant confuse an article on sauce with its cooking instructions. Wikishagnik (talk) 21:11, 4 February 2012 (UTC)

• Merge with affine algebraic curve i don't see why this article deserves a whole page, then every exception to every mathematical formula will get a new page. I still hold on to Delete because their is nothing encyclopedic about this article. Its just a concept. — Preceding unsigned comment added by Wikishagnik (talk • contribs) 20:57, 4 February 2012 (UTC)

"Just a concept": We have many articles that are "just" about "concepts". That's a silly reason to vote delete. Sławomir Biały (talk) 13:12, 7 February 2012 (UTC)

• Merge: This is not a candidate to move to Wiktionary but notability is still borderline. The term does have some traction in the literature, though most of the sources I found defined it for a variety rather than just a curve as given in the article. I could not find any sources that were accessible to someone without a degree in algebraic geometry, or more specifically I couldn't find any secondary sources, so I think this subject is more suitable for a section of larger article than for an article on its own. The article as it is does have a number of serious issues, lack of sources being the most serious, but also the article consists simply of a definition and an example, so notability aside it would be better to include it in another article until there is enough material to do a split. I'd suggest Resolution of singularities as a merge target but there may be better ones.--RDBury (talk) 20:59, 4 February 2012 (UTC)

  Nope. First, smooth completion (compactification) may involve resolutions of singularities (e.g. where a curve has self-intersections at infinity), but is not always the case. There are no singularities in curves $y=x$ or $y^2=x^2+1$, but their compactifications are non-trivial. Second, the article "resolution of singularities" is about various methods, by contrast with "smooth completion" where blowing up is always used. Incnis Mrsi (talk) 21:35, 4 February 2012 (UTC)

• Speedy keep: widely used term, see here. It would be nice however to add some references. Sasha (talk) 21:03, 4 February 2012 (UTC)

Getting hits on Google scholar is not a criterion for keep. First, are you getting hits on the actual topic or hits on the same phrase being used with a different meaning? You have to actually follow the links and understand what they say to make that determination. Also, are any of the hits for secondary sources? Again you have to follow the links and determine if they are primary research. WP shouldn't have articles where only a few researchers can verify their accuracy.--RDBury (talk) 20:07, 5 February 2012 (UTC)

The material is in Hartshorne chapter 4, a standard reference (see current version of article). Tkuvho (talk) 08:21, 7 February 2012 (UTC)

Exactly where in Hartshorne is the term "smooth completion" used? Does he call it something else? Sławomir Biały (talk) 13:12, 7 February 2012 (UTC)

@RDBury: Well, I am not an expert in algebraic geometry, but I hope I am not totally incompetent. Obviously, I have looked through the some of the links (to the best of my modest ability) before posting the link to google hits here. Most of the links that I saw are secondary sources which refer to the same mathematical object which is discussed in the article.

As to accuracy, the same reasoning can be used (and has been used) to argue that there should be no technical mathematical articles on Wikipedia at all. Sasha (talk) 14:50, 7 February 2012 (UTC)

• Keep. The page requires expansion but is obviously a notable subject. Tkuvho (talk) 21:05, 4 February 2012 (UTC)

I maybe — Preceding unsigned comment added by Wikishagnik (talk • contribs) 21:11, 4 February 2012 (UTC)

• Merge to affine algebraic curve if it can't be significantly expanded with references; it's just too short and dict def like as it is, though yes not the sort of definition that would be welcome at wiktionary.--JohnBlackburne^words_deeds 02:31, 5 February 2012 (UTC)

  Merge to which article? Did you walk through the link affine algebraic curve, yourself? Incnis Mrsi (talk) 08:05, 5 February 2012 (UTC)

• I'm leaning towards keep. Assertions that the article has no possibility of expansion seem farfetched to me. A glance at some of the scholar hits shows, for instance, that researchers also talk about smooth completions of higher-dimensional varieties. So right there is something that could be used to expand the article (and also make the merge targets so far proposed inappropriate). Sławomir Biały (talk) 13:12, 7 February 2012 (UTC)

• Comment: Perhaps I should add a comment concerning how important smooth compactifications are (and Smooth completion appears to be a special case/synonym though I've never heard the term). Off the top of my head, here are just a few names of people who have put a lot of effort into constructing smooth compactifications (of Shimura varieties): Deligne–Rapoport, Faltings–Chai, Mumford, Katz–Mazur. And I'll just stop there, that's 3 Fields medalists already. This subject is extremely important in the whole Langlands/Serre automorphic/Galois representations business. RobHar (talk) 17:42, 7 February 2012 (UTC)

The article "Variations of Hodge structures of a Teichmüller curve" by M Möller in J. Amer. Math. Soc. 2006 uses the term "smooth completion". Tkuvho (talk) 18:00, 7 February 2012 (UTC)

What I meant to say was that before this AfD, I had never heard of "smooth completion", though when I searched for it on the google I found many results. The difference in terminology seems to be partially a difference between which field of math you're reading. Another difference may be that "complete" is usually used for varieties, so if you are looking at more general things (which may not even be schemes), you might use "compactification" (as a synonym of the never-used "properification"). From looking at a few papers it seems like a "smooth completion" of U might be a variety V that has a divisor D which has locally normal crossings and such that V\D = U. One might use "smooth compactification" more generally. RobHar (talk) 19:05, 7 February 2012 (UTC)

• Keep but possibly move to smooth compactification (183 hits on MathSciNet vs only 26 for smooth completion, and a little more general as RobHar says). There is an entire book on this topic: Ash, Mumford, Rapoport, and Tai, "Smooth compactifications of locally symmetric varieties", 2nd ed., Template:MR. To me that seems convincing enough evidence that it can stand alone. And the article has been significantly improved since it was first nominated. —David Eppstein (talk) 03:34, 8 February 2012 (UTC)
• changing my !vote to keep based on it's current expanded state, per David Eppstein and others.--JohnBlackburne^words_deeds 03:39, 8 February 2012 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.