Talk:Period mapping

There are no article titled as "Griffiths' transversality" or "Griffiths transversality theorem" from neither this article nor "Hodge structure"!

A little while ago, on the talk of "Gauss-Manin connection" someone asked "How do we relate Gauss-Manin connection to the variation of Hodge structure?" Example of period mapping of elliptic curves in this article would appear as the Picard-Fuchs equations of Gauss-Manin connection. On the article there are few information about the relation to Hodge structure, which need more homological algebraic treatments.

Kodaira-Spencer map would also relate period mappings closely. --Enyokoyama (talk) 07:48, 17 March 2013 (UTC)

Ehresmann's theorem

The words "period mapping" do not appear in this section or in the article Ehresmann's theorem. What is the connection? Reak spoughly (talk) 09:02, 21 March 2013 (UTC)

Concepts of fiber bundles and connections was developed by Cartan and Ehresmann in 1940's and 1950's. As you say, there were no relationship to Ehresmann's theorem at first glance, and no word "period mapping" in the section. However, period mapping, which appeared in Abelian integral, has no modern interpretation until the idea of ​​connection and fiber bundle. In particular, the path from b to 0 in the last of this section realizes the path of the integral and so it is natural that there are the name of Ehresmann at the top of this article, I think. Rather than Ehresmann's theorem, then you should visit the article of Ehresmann connection might be good.--Enyokoyama (talk) 13:30, 21 March 2013 (UTC)