Talk:Abel–Jacobi map
From Wikipedia, the free encyclopedia
 |
|||||
| Mathematics rating: | B Class | Mid Priority | Field: Geometry | ||
| Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article. | |||||
[edit] Proposed merge with Abel's curve theorem
Seeing this merge notice reminded me of a more important potential merge: with Jacobian variety, since so much of the material depends on the explicit definition of the Jacobian. I don't know anything about these classical theorems (it's an accident, really, that I know the classical version of the Abel-Jacobi map rather than the modern one) so I don't know why Abel's curve theorem is related to the Abel-Jacobi map. Seems to me it should really be placed in Abelian integral. Note that all four of these articles need significan expansion and are rather stubbish at the moment. However, as a look over them it seems clear that they should all be tied into Jacobian variety, since that is the unifying feature and will create a node that will hopefully attract some potential editors (rather than letting them find these isolated stubs). At the moment I think that the relationship of all of these articles to Jacobian variety is stronger than their relationships to any of each other, and that this is the logical place, at the moment, to link or merge them. Charles Matthews: you proposed this merge; could you give your thoughts on slapping a merge-with-Jacobian variety notice on these, rather than the current one? Ryan Reich 22:02, 12 July 2007 (UTC)
I see no reason for such a merger. Furthermore, in my field, the Abel-Jacobi map is much better known than Abel's curve theorem.
Moreover, there is an invariant definition of the Abel-Jacobi map that does not require choosing a basis in cohomology. Somebody should add it to the article. Katzmik 09:50, 1 August 2007 (UTC)
