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Perhaps I missed it, but it seems to me that the semi-positive condition has not been emphasized here. The pseudocycle construction requires the compactified moduli space to have "boundary" of co-dimension 2. In general, this is not true. One must put conditions on the Chern numbers of spheres that can bubble off, hence the semi-positivity condition used in e.g. McDuff-Salamon. SammyBoy 05:07, 10 April 2006 (UTC)
You are right. The simplest fix is to assume semipositivity. Perhaps we should say "under suitable/reasonable assumptions" the boundary can be shown to have codimension at least 2. Taken literally, this is a vacuous statement, so perhaps we should at least define semipositivity and explain how it's used? I'm never sure how much precision is desirable in an encyclopedia article as difficult as this. Your improvements are welcome. Joshua Davis 19:30, 10 April 2006 (UTC)
Sorry I disappeared for so long. How about under "some simplifying assumptions on the geometry of the symplectic manifold" ? I think you are right that too much precision is undesirable. On the other hand, the huge amount of work that has been done in trying to explain and formalize the virtual moduli cycle would seem like a waste of time without some precision. (This basically is the construction of something like a fundamental class of the moduli space of pseudoholomorphic spheres, even though the boundary strata may be of too high a dimension. I don't understand it, alas.) SammyBoy 07:49, 16 September 2006 (UTC)
The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.
The result of the move request was: Not moved. The proponent did not make the reason for the move very clear. At least there should be a proper reference saying that 'space of stable maps' is the usual name. EdJohnston (talk) 04:55, 14 January 2014 (UTC)
Stable map → Space of stable maps – As far as I understand, the object of study is a "space of stable maps" (in fact, stack), which is a generalization of the moduli space of stable curves. Taku (talk) 12:58, 17 December 2013 (UTC)
I don't think that this is a really pressing issue, but I also have no objection. It's fine by me. Mgnbar (talk) 22:40, 17 December 2013 (UTC)
Comment how are we going to find out where exactly Jesus' manger was if there's no WP article on stable maps? RedSlash 05:54, 19 December 2013 (UTC)
Agree with Red Slash. --SmokeyJoe (talk) 04:33, 30 December 2013 (UTC)
I also agree with Red Slash. Indeed, as Taku pointed out, there is no description about the relationship to the concept of "stack" in this article. It should be written in the headline or the paragraph Deligne-Mumford stable mapping space, I think. For example, "the space of stable mapping inevitably reaches to the idea of 'stack' by compactificacation." But their explanations may be difficult.--Enyokoyama (talk) 05:44, 30 December 2013 (UTC)
I have no idea what's going on here. What's a stack? --BDD (talk) 19:16, 8 January 2014 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.