Talk:Function of several complex variables
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Vote for new external link
Here's my website full of example problems from complex variables. Someone please put it in the external links section if you think it's helpful!
http://www.exampleproblems.com/wiki/index.php/Complex_Variables
- Not relevant, the link is about 1 variable, not several, like this article. Oleg Alexandrov (talk) 02:47, 29 December 2005 (UTC)
- Agree with Oleg — not relevant. - Gauge 00:23, 8 January 2006 (UTC)
- When several complex people agree on the same thing, it must be true! :) Oleg Alexandrov (talk) 02:32, 8 January 2006 (UTC)
Deformations of complex structures
On the sixth paragraph (the one that starts "from this points onwards there was a foundational theory...") mentions deformation theory of complex structures. Why is this on the foundations of the theory? I would find it quite interesting if a reason for the study of deformations of complex structures was given - and why it is considered to be one of the pillars (foundations) of the subject.
I would also find it quite nice if some applications of several complex variables to PDEs were mentioned.
I think that if this, quite nice, entry on several complex variables would include these two things, it would become even more enlightening. — Preceding unsigned comment added by 155.198.157.113 (talk • contribs) 18:57, 21 July 2006
Typesetting reversion
I reverted since there was an inconsistent mixture of typography: LaTeX and {{bigmath}}/{{math}} for inline and displayed formulae. The IP cleaned up the mixture. I'll check in detail if there were any typos the IP introduced in his/her edit, which may have motivated this reversion by Incnis Mrsi. M∧Ŝc2ħεИτlk 14:01, 17 June 2013 (UTC)
- Could you look for IP’s user_talk before igniting an edit war? I reverted and will revert unconditionally an illegible crap like “−I”. The “imaginary unit i” also looks ugly, although I would not revert it were this one the only degradation. BTW, I do not see anything bad with “LaTeX and {{bigmath}}/{{math}} mixture of typography”: the purpose of {{math}} is namely to match appearance of <math> more closely than wiki code does. Incnis Mrsi (talk) 14:48, 17 June 2013 (UTC)
- Also, consult WP:MOSMATH #Blackboard bold please. There are plenty of article where formatting is really poor. Why people like you and 99.241.86.114 start quarrels over typesetting preferences in relatively clean articles? Incnis Mrsi (talk) 14:59, 17 June 2013 (UTC)
- I don't want to start an edit war, nor quarrel over my own preferences, just trying to to clean up the silly mix is all. You say this is a "relatively clean" article when LaTeX, HTML, and WP templates are used all over the place (LaTeX is inline and {{math}} displayed). As for the pointer to WP:MOSMATH, the article has a mix of Cn and , so tried to make them all consistent as blackboard bold - if others insist they could all be changed to bold after. M∧Ŝc2ħεИτlk 15:06, 17 June 2013 (UTC)
- I do not obstruct any change which unambiguously improves at least something and does not make any demonstrable harm to the rest of code. Incnis Mrsi (talk) 15:16, 17 June 2013 (UTC)
- I don't want to start an edit war, nor quarrel over my own preferences, just trying to to clean up the silly mix is all. You say this is a "relatively clean" article when LaTeX, HTML, and WP templates are used all over the place (LaTeX is inline and {{math}} displayed). As for the pointer to WP:MOSMATH, the article has a mix of Cn and , so tried to make them all consistent as blackboard bold - if others insist they could all be changed to bold after. M∧Ŝc2ħεИτlk 15:06, 17 June 2013 (UTC)
I tried again in this edit, and assumed bold was the preference instead of blackboard bold for the real and complex number sets . M∧Ŝc2ħεИτlk 10:36, 18 June 2013 (UTC)
Too technical
I hope it's OK that I added the "technical" template at the top of the article. The reason is that the article doesn't give an overview that's comprehensible to someone who isn't already quite familiar with the subject. The lead is fine, but the next paragraph assumes intimate familiarity with the subject. The article could really do with a first section that introduces the subject to someone who's familiar with the prerequisites (e.g. single-variable complex analysis, multivariable real calculus) but who hasn't studied multivariable calculus per se. (Unfortunately I cannot write such a section, as I am a member of this target audience.) Nathaniel Virgo (talk) 13:05, 3 January 2015 (UTC)
- You need to be still more specific. The paragraph following the lead is in the history section. Such a section is not even intended to be understood mathematically (for those unfamiliar with the subject). The section after that is on ℂn. Is it here you get stuck? YohanN7 (talk) 16:40, 3 January 2015 (UTC)
- I've moved the paragraph "The Cn space" to the last, because it brings an example of Stein manifold but it needs a lots of efforts to reach it. Cousin problem, Levi problem, and the development of several complex variables must be explained, I think.--Enyokoyama (talk) 10:00, 23 March 2015 (UTC)
Assessment comment
The comment(s) below were originally left at Talk:Function of several complex variables/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
| Needs splitting into sections, comparisons with single-variable case, examples, why they are "supposed to be" analytic, etc. Tompw 13:29, 20 November 2006 (UTC) |
Last edited at 12:08, 16 April 2007 (UTC). Substituted at 02:35, 5 May 2016 (UTC)
Fix the ambiguous use of "these" and "they"
If the intended meaning of the first paragrah is that the theory of several complex variables studies only holomorphic functions then first sentence in the paragraph should say so. As the current article stands, the first sentence speaks of complex valued functions on complex n-tuples. The next sentence in the article says that "these functions" are "not just any functions". It is unclear which functions "these functions" refers to.
It would be clearer if the article began: "The theory of several complex variables deals with with a special type of complex valued functions on n-tuples of complex numbers. The functions of this special type are the holomorphic functions." - if that is the intended meaning.
Series name
Considering the relationship with Cauchy's integral formula, I think it is good to use the page of Laurent expansion for explanation, but since it is a holomorphic point, I would like to describe it as Taylor expansion, Is there a good way?--SilverMatsu (talk) 12:53, 7 November 2020 (UTC)
I would like to merge a Holomorphically convex hull into Several complex variables
Holomorphically convex hulls are necessary to understand the properties that occur when increasing complex variables from one to several.So I wanted to add this topic to this page, but when I tried to add it, I noticed that the contents of the two pages were covered. I think the reason I came to think of the Holomorphically convex hull property was about the convergence region when the conditions described on the Holomorphically convex hull page were applied to the analytic function (holomorphic function).(Affects analytic continuation.) The power series is written on this page, so I would like to add a clause called Holomorphically convex hull on this page to integrate it. I would to leave the Holomorphically convex hull page as a redirect as a provisional. ( i.e. I do not object to increasing the content of the page and recreating a Holomorphically convex hull page.). thanks.--SilverMatsu (talk) 07:55, 17 November 2020 (UTC)
- I completely changed my response here, sorry about that. This is fine with me, though I still believe it should all be merged into complex analysis. I have added templates that signify some of the problems I see with the article. In the eventuality that it is merged, many of them can be ignored. However, we do have to fix all the reference problems to make sure there is no original research. Thanks! Footlessmouse (talk) 08:59, 17 November 2020 (UTC)
- Thank you for your feedback.I can't answer to the lead sentence because I didn't create it.The section on holomorphic functions supports your suggestion in the same part as in the case of one variable, and you may not need to distinguish it from one variable or several variables simply by saying complex analysis.On several variable pages, I added a note of order of integration because someone had already created a holomorphic function section, but personally, I think it's good to write on the complex analysis page.Unlike the case of one variable, there is no isolated zero of the holomorphic function, so the condition for establishing the identity theorem requires annotation.I think we need to consider a link to the identity theorem.Coherent sheaf, Hartogs' phenomenon, etc. are separate pages, so it seems that the reason why this page exists independently is weakening.I strongly agree that this page needs to be fix.I also understand that consolidating pages will increase the number of participants and improve the quality of the pages. Thanks!--SilverMatsu (talk) 09:55, 17 November 2020 (UTC)
- SilverMatsu, that makes sense to me. I apologize for my slurry of comments. When I reread the original, I realized it did not have the right tone. It sort of seemed like I was yelling about it and being a little too aggressive, when you were certainly not the right person to yell at (not that anyone is). So my apologies. I appreciate the work you are doing, keep it up! Footlessmouse (talk) 10:34, 17 November 2020 (UTC)
- Footlessmouse Don’t worry about it. Thank you for contributing to the article with a wealth of knowledge.--SilverMatsu (talk) 11:18, 17 November 2020 (UTC)
- SilverMatsu, that makes sense to me. I apologize for my slurry of comments. When I reread the original, I realized it did not have the right tone. It sort of seemed like I was yelling about it and being a little too aggressive, when you were certainly not the right person to yell at (not that anyone is). So my apologies. I appreciate the work you are doing, keep it up! Footlessmouse (talk) 10:34, 17 November 2020 (UTC)
I would like to merge the Reinhardt ___domain into Several complex variables
For the same reason as in the previous section.Oddly, it wasn't linked from this page.--SilverMatsu (talk) 12:08, 18 November 2020 (UTC)