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Silvermatsu (talk | contribs) It's been a month since the discussion ended, so I think it's okay to archive it. |
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I forgot to say it. Redirecting to the title of this page instead of section redirecting to the ___domain of holomorphy is also a suggestion choice.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 05:39, 21 December 2020 (UTC)
:I don't think I agree with the assertion that several complex variables is distinct from complex analysis in one variable only in the sense that it is the study of domains of holomorphy/Stein manifolds. The interesting phenomena that occur in several complex variables are fundamentally important to the study of compact complex manifolds and projective complex varieties for example, and has a different flavour to complex analytic geometry in <math>\mathbb{C}^n</math> or on Stein manifolds, which is what the current lead gives most of its weight to.
:I don't think it is standard anywhere to refer to the theory of complex functions of several variables as "domains of holomorphy theory" so Wikipedia should definitely avoid presenting that as the main name of the subject. As you point out however, people do refer to "several complex variables" and that is the title of the main book on the subject, so that is surely the better name for the article. I think we probably agree that the area is different enough in flavour to complex analysis of a single variable that it deserves its own article. I wouldn't be opposed to merging with [[complex analysis]], which is quite a thin article, but I don't think there is any particular need to. In particular I think complex analysis of a single variable gets a very different (and much broader) treatment pedagogically, and that is an article looked at frequently by people who are not pure mathematicians interested in several complex variables (engineers, physicists) and presenting all the definitions on that page in their largest generality would serve more to obfuscate the point rather than elucidate it for most visitors. Just my two cents. Thank you for improving the articles in complex analysis! [[User:Tazerenix|Tazerenix]] ([[User talk:Tazerenix|talk]]) 05:53, 23 December 2020 (UTC)
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