Talk:Algebraic geometry and analytic geometry

Analytic self maps of Riemann sphere?

 * Section added. —Nils von Barth (nbarth) (talk) 07:00, 7 December 2009 (UTC)

In the example of analytic self maps of the Riemann sphere, what exactly is meant by analytic? The definition I recall, perhaps wrongly, from my undergraduate days would imply that rational functions are analytic maps from the Riemann sphere to itself, which seems to contradict the current version of the article. NowhereDense (talk) 07:22, 20 October 2008 (UTC)

The polynomials are precisely the maps of the Riemann sphere such that infinity is the only point mapped to infinity. —Preceding unsigned comment added by 24.61.44.63 (talk) 12:25, 29 November 2008 (UTC)

This discussion is important and should be merged to the article. As of now the statement in the article is erroneous. 147.96.18.189 (talk) 12:13, 21 May 2009 (UTC)

Request for references
It would be very nice to have a reference for the Leftschetz principle (if not its own article) --Konrad (talk) 03:10, 21 January 2010 (UTC)

Thanks to Charles Matthews, there are references for the Leftschetz principle now :-) --Konrad (talk) 00:13, 22 January 2010 (UTC)

Scheme were not defined when GAGA was published
Section "Formal statement of GAGA", which is supposed to present the result of Serre's article begins with "Let $$ (X,\mathcal O_X) $$ be a scheme of finite type over C". GAGA was published before the definition of schemes by Grothendieck. Therefore the use of schemes in this section is misleading, by suggesting that it is a result about schemes. This is also too technical for people that are not accustomed with scheme formalism. I recall that searchers, students and users of analytic geometry (as well as a large part of searchers, students and users of algebraic geometry) do not use scheme formalism. D.Lazard (talk) 11:21, 11 March 2013 (UTC)

Thanks
Dear R.e.b. Thanks for you making the new article "Moishezon manifold," independent on this article.--Enyokoyama (talk) 15:34, 15 June 2013 (UTC)

to avoid too technical description, add a new paragraph
To avoid too technical description, I add a new paragraph "Main statement", which summarize the formal statements. Perhaps, the paragraph "Formal statements" might make this article too technical. But they are indeed true.--Enyokoyama (talk) 20:04, 19 September 2014 (UTC)


 * I revised your paragraph. I think I made it even less formal but still accurate.  Ozob (talk) 03:57, 20 September 2014 (UTC)


 * Welcome Ozob's revision! I'm sure that it would be more acceptable for many people. Thank you.--Enyokoyama (talk) 06:52, 20 September 2014 (UTC)

Oka's Coherence theorem
If this is irrelevant please delete this comment/section. Does Oka's coherence theorem apply to the seemingly more general case of complex analytic spaces, or only to the structure sheaf of a complex manifold? Perhaps X^(an) is always a complex manifold? This comment is in reference to the use of Oka's theorem in the "Main statement" section. My apologies if this question is too naive. — Preceding unsigned comment added by 2601:2C1:200:1BE0:7C4B:764E:6C98:9007 (talk) 00:44, 25 March 2019 (UTC)