Talk:Kodaira dimension

Comments

"V" and "R" apparently survive this article without ever being defined. 131.111.213.32 (talk) 14:31, 6 December 2009 (UTC)[reply]

Fixed. Not particularly elegantly, though; this article needs serious work. Ozob (talk) 02:08, 7 December 2009 (UTC)[reply]

Dear　Professor BTotaro! Thanks for your improvement about this article. In particular, ? -> Calabi-Yau 3-fold and ? -> rational 3-fold, Fano variety and so on. Calabi-Yau condition is a little more strict than those using in physics but there is no problem to substantially, I think. Would you mind checking the article "Iitaka dimension" in which I'd write about Iitaka conjecture (additional formula for Iitaka fibration). I'm neither researcher nor professor.--Enyokoyama (talk) 08:32, 5 November 2013 (UTC)[reply]

"citation needed" in headline

"Citation needed" in the headline may ask when and who defines the notation κ of Kodaira dimension. I don't know when and who defines it but I'm sure that in the seminar Shafarevich 1965 Kodaira dimension κ had been appeared. Rather, it is more serious problem that at that time mathematicians in CCCP had let Kodaira dimension of ruled and rational varieties be -1. If so, then Iitaka conjecture (additive formula on fibered structure) would not hold. It should be -∞ and Iitaka conjecture holds.--Enyokoyama (talk) 10:12, 17 April 2014 (UTC)[reply]

Yesterday, Mr. Noellapin taught me the URL of Professor Iitaka, who defined and named “Kodaira dimension” in early times of 1970s. It states that the description about who and in which paper named "Kodaira dimension" in the headline of this article is mistaken.　http://www-cc.gakushuin.ac.jp/~851051/second3j.pdf (but in Japanese)

Today, I have seen the original seminal paper in Russian published in 1965 by Shafarevich and others, and read the translated into English one published in 1967 by AMS. It is sure that "κ" without the naming “Kodaira dimension” is appeared in the introduction and other chapters of them. But I cannot find the explanations about the meanings and prospects of "κ" in them as the "Kodaira dimension." Though Kodaira dimension might be based on the idea of genus in topology, It is vastly enlarged in order to classify algebraic varieties and study their structure.

I will try to modify the headline of this article and write the new paragraph on "On the naming of Kodaira dimension." Let me take for a moment to do it.--Enyokoyama (talk) 13:42, 18 April 2014 (UTC)[reply]

Exterior powers of a vector bundle

I'm well acquainted with the exterior algebra of differential forms on a manifold, but I have not yet encountered taking exterior powers of a vector bundle (until this article).

Clicking on the link took me to Exterior algebra, which says virtually nothing about exterior powers of a vector bundle.

I suggest the article should have at least a brief explanation of what this means. If not, then since there is no place in Wikipedia for unexplained concepts, that section ought to be deleted.2600:1700:E1C0:F340:B986:5EB6:7508:AD86 (talk) 07:22, 2 June 2019 (UTC)[reply]