Talk:Abel–Jacobi map

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Mathematics rating:
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 Field: Geometry


I left a note at Abel-Jacobi map as well, but I can't let this one go without one. Whatever happens with regard to my suggestion there, I think that before merging this thing anywhere it should be improved a lot. The sentence (!) itself is quite impenetrable and it doesn't give any indication why it should be related to the Abel-Jacobi map (though one can guess) or indeed, just about anything else. Ryan Reich 22:12, 12 July 2007 (UTC)

A reaon for incoherence[edit]

Well, one reason it may appear incoherent is that it's almost identical with the Mathworld article with the same name. DavidCBryant 17:43, 13 July 2007 (UTC)

The seventeen-year-old part of me (the part that used to read MathWorld like I now read Wikipedia) wants to protest, but...I agree. Too bad, really; math is so easy to write poorly, not as easy to write well. Ryan Reich 20:06, 13 July 2007 (UTC)

I also directly cited that material as the reference for the article. It was my understanding that Mathworld content was released under GFDL.--Cronholm144 18:30, 13 July 2007 (UTC)

I also figured something like that since we do seem to be inspired by MathWorld a lot, but if you go to "Terms of Use" in the small print at the bottom of any article there, you'll find that they are not at all free and open. Ryan Reich 20:04, 13 July 2007 (UTC)
I have gone through and tagged the articles that I created. I was confused because I had seen other "inspired" content (i.e. copying) from mathworld, and I figured that it was GFDL like planetmath (bad assumption to make).--Cronholm144 05:04, 14 July 2007 (UTC)

Proposed merge with Abel's curve theorem[edit]

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)