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arXiv · 0706.1381

A geometric invariant theory construction of moduli spaces of stable maps

Elizabeth Baldwin·David Swinarski
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Abstract

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.

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Elizabeth Baldwin, David Swinarski. 2007-08-27. A geometric invariant theory construction of moduli spaces of stable maps. https://doi.org/10.1093/imrp%2Frpn004

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