Talk:Complex geometry

I am tempted to redirect this to complex plane. The fundamental theorem has nothing to do with geometry, and Gauss' ruler-and-compass constructions were not proved using complex numbers to my knowledge. If those to items are removed from the article, there's really nothing much left. The geometry of complex numbers is already explained in complex number. AxelBoldt 19:47 Feb 22, 2003 (UTC)

Well, it sounds like a good idea... but we'd need an actual article at Complex plane instead of a redirect to complex number! -- Tarquin 21:47 Feb 22, 2003 (UTC)

If this is supposed to be about the geometry of the complex plane, then perhaps prominence should be given to the fact that the only holomorphic bijections of complex projective 1-space to itself are linear fractional transformations, which preserve circles (a straight line being regarded as a circle that passes through the point at infinity). Michael Hardy 21:50 Feb 22, 2003 (UTC)

Actually, in mathematics proper, "complex geometry" is the study of complex manifolds and functions of many complex variables. Every year, there are tens (I would estimate as about 50) conferences on "complex geometry" (please check the Google).

The definition "application of complex numbers to plane geometry" is useless, misleading and should be removed somewhere - to "complex plane" for instance. A quick search in Google shows that everywhere (except Wikipedia) complex geometry means "study of complex manifolds and functions of many complex variables". It's hard to guess where the authors of the article as it is now came at their definiton, Google does not find anything similar.

Unless there are reasonable objections, I remove the present content to "complex plane". Tiphareth 15:08, 16 September 2006 (UTC)

Removed former content to Complex analytic geometry. Compare with French and Italian pages (inter-wikied), it's clear that "complex geometry" is geometry of complex manifolds and not application of complex numbers to secondary school plane geometry. Tiphareth 16:47, 2 April 2007 (UTC)

On confusing and unclearness

I'd described something about the notations in this article. For the reason to describe holomorphic bundles it may be something unavoidable　to describe the definitions of line bundles and divisors. However, the other things may be required to be described in this article, for example, complex deformations, harmonic analysis, and Hodge theory. I think.--Enyokoyama (talk) 08:11, 11 July 2014 (UTC)

Vast room for improvement in this article

Most of this article is written as though the writer has no interest in whether the writing is understood by anyone other than a specialist in a nearby field to complex geometry.

There are so many places where the addition of just a few more words would greatly improve the clarity. (For just one obvious example: How about telling readers what the group operation is in the Picard group?)

Terrible writing like this does not help many readers.128.119.202.144 (talk) 18:00, 5 October 2019 (UTC)

That’s a very fair critique. I tend to view the article at the current status to be a very early draft. Material-wise, there are still SO much more to cover, in addition to the writing quality. — Taku (talk) 23:22, 5 October 2019 (UTC)

I have made some effort to improve the page by adding plenty of discussion about the ideas behind complex geometry and the actual definitions of objects studied in the area. The sections on line bundles and divisors, and complex vector bundles have been removed, as this is not the right page for that content, and it was not up to scratch in any case. The page could do with a history of the theory of complex geometry, but it is in significantly better shape now than before.Tazerenix (talk) 23:26, 7 January 2020 (UTC)