Talk:Gromov–Witten invariant

I just fixed an anonymous edit, which seemed well-intentioned but didn't work so well. Essentially the editor made two changes. First, s/he changed notation from n to k; both are used in the subject, but n is used in the stable map article, so I think n should be kept. Also, the editor did not thoroughly do the change, but petered out in the middle. Second, s/he confused the moduli space of curves M_{g, n} (which has nothing to do with the target X) with the moduli space of maps M_{g, n}(X, A). I have explicitly written the latter into the article, in an attempt to clarify. Also, it is undesirable to fix the domain, \Sigma, as the editor did, since we want to consider maps on all domains in M_{g, n}. If the edit was sincere and I'm wrong, let me know; we can work it out. Joshuardavis 16:47, 3 October 2005 (UTC)[reply]

Unfortunately, this article is imprecise in many respects, explains some things very badly, or tries to explain things that are just impossible to explain in such an article. I am not sure what should be done about this, as it would require a lot of work to improve it. --Arend Bayer. (I am a math Post-doc working among other things on Gromov-Witten invariants in algebraic geometry.)

Hi, Arend. Advanced math articles on Wikipedia tend to be quite imprecise/intuitive/incomplete. They can aspire only to work out the landscape. See for example Floer homology. Hmm, this article has some bad parts, such as the obstruction bundle. Also, the treatment is entirely symplectic, which makes it seem even worse to an algebraic geometer, I imagine. It would be nice to have an algebraic treatment... Joshua R. Davis 04:35, 8 March 2007 (UTC)[reply]

Is this correct?[edit]

The statement:

The evaluation map sends the fundamental class of M to a d-dimensional rational homology class in Y, denoted

The articles defines Y = M \times \sigma^k. The evaluation map is from Y to X^k; so, how could the ev map send a class in M to a class in Y? 15:30, 7 February 2008 (UTC) User:155.198.157.118

I think you have a couple of typos there. The evaluation map being used here goes from StableMaps to StableCurves x X^k. I have adjusted the article to make it all more explicit. Let me know if there is an error. Joshua R. Davis (talk) 17:17, 7 February 2008 (UTC)[reply]

I had a typo; that should be X^n, not X^k. Joshua R. Davis (talk) 18:45, 7 February 2008 (UTC)[reply]

Extended Technical Discussion Needed[edit]

This page should have more information about the basic technical details for Gromov-Witten theory. A good reference for this material is http://www.math.columbia.edu/~ccliu/GWsummer17/GWsummer17.html — Preceding unsigned comment added by 71.212.185.82 (talk) 05:30, 17 August 2017 (UTC)[reply]