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arXiv:0706.1381 [math.AG]AbstractReferencesReviewsResources

A geometric invariant theory construction of moduli spaces of stable maps

Elizabeth Baldwin, David Swinarski

Published 2007-06-11, updated 2007-08-27Version 3

We construct the moduli spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT). This construction is only valid over Spec C, but a special case is a GIT presentation of the moduli space of stable curves of genus g with n marked points, \bar M_g,n; this is valid over Spec Z. Our method follows that used in the case n=0 by Gieseker to construct \bar M_g, though our proof that the semistable set is nonempty is entirely different.

Comments: 75 pages LaTeX; the GIT construction of moduli spaces of stable n-pointed curves is now given over the integers
Journal: International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn004, 104 pages
Categories: math.AG
Subjects: 14H10, 14D22, 14N35
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