A geometric invariant theory construction of moduli spaces of stable maps

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.

arXiv comment75 pages LaTeX; the GIT construction of moduli spaces of stable n-pointed curves is now given over the integers

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Cited by in corpus (8)

• Good moduli spaces for Artin stacks
• Hilbert-Mumford criterion for nodal curves
• Birational contraction of genus two tails in the moduli space of genus four curves I
• GIT Constructions of Moduli Spaces of Stable Curves and Maps
• Groebner techniques for low degree Hilbert stability
• GIT and moduli with a twist
• Modular compactifications of ${\mathcal{M}}_{2,n}$ with Gorenstein singularities
• GIT stability of weighted pointed curves