Talk:Quantum cohomology

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It must be described that the big quantum cohomology ring is intimately related to Gromov-Witten potential. And it also brought new results and opened the window toward the new sight for enumerative geometry. --Enyokoyama (talk) 15:35, 12 March 2013 (UTC) In the origin of quantum cohomology it is important that quantum cohomology represents the cup structure variation of them, in particular, homology class A∈H2(X;Z) which relates closely to the number of rational curves in quintic threefold.--Enyokoyama (talk) 04:39, 13 April 2013 (UTC)[reply]

The idea of quantum cup product as a deformation of the ordinary cup product is discussed in the section "Geometric interpretation". Mgnbar (talk) 13:10, 13 April 2013 (UTC)[reply]

Thanks for your findings. But as its application using mirror symmetry the number of rational curves on quintic three-fold is described by integration of some periods (on B model). Kontsevich and Manin illustrated some higher degree terms of them. What I'm wondering is that I should write them in the article of enumerative geometry or of this article.--Enyokoyama (talk) 17:58, 13 April 2013 (UTC)[reply]

I'm not sure; it depends somewhat on what you write. The subject of enumerative geometry is older and bigger than GW/QC theory, and the article Enumerative geometry should serve as a survey and introduction to that whole subject. So that article should mention, but not go into detail about, GW and QC. If you want to write something detailed, then this article or Gromov-Witten invariant is probably a more suitable place for detail. Mgnbar (talk) 18:44, 13 April 2013 (UTC)[reply]