A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps

Abstract

We construct the moduli spaces of stable maps, ⁠, via geometric invariant theory (GIT). This construction is only valid over ⁠, but a special case is a GIT presentation of the moduli space of stable curves of genus g with n marked points, ⁠; this is valid over ⁠. In another paper by the first author, a small part of the argument is replaced, making the result valid in far greater generality. Our method follows the one used in the case n = 0 by Gieseker in [9], 1982, Lectures on Moduli of Curves to construct ⁠, though our proof that the semistable set is nonempty is entirely different.

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