Baldwin, Elizabeth; Swinarski, David A geometric invariant theory construction of moduli spaces of stable maps. (English) Zbl 1155.14009 IMRP, Int. Math. Res. Pap. 2008, Article ID rpn004, 104 p. (2008). Let \(\overline{M}_{g, n}({\mathbb{P}}^r, d)\) be the Kontsevich–Manin coarse moduli space of stable maps of degree \(d\) from \(n\)-pointed genus \(g\) curves into the \(r\)-dimensional projective space \({\mathbb{P}}^r\). The authors construct \(\overline{M}_{g, n}({\mathbb{P}}^r, d)\) via geometric invariant theory. The method follows the one used in the case \(n=0\) in [D. Gieseker, Lectures on moduli of curves. Lectures on Mathematics and Physics. Mathematics, 69. Tata Institute of Fundamental Research, Bombay. Berlin-Heidelberg-New York: Springer (1982; Zbl 0534.14012)], but the proof that the semistable set is nonempty is entirely different. The construction is only valid over \(\text{Spec}\,{\mathbb{C}}\), but a special case, a GIT presentation of the moduli space of stable curves of genus \(g\) with \(n\) marked points, is valid over \(\text{Spec}\,{\mathbb{Z}}\). Reviewer: Vladimir L. Popov (Moskva) Cited in 2 ReviewsCited in 5 Documents MSC: 14D20 Algebraic moduli problems, moduli of vector bundles 14H10 Families, moduli of curves (algebraic) Keywords:moduli space; geometric invariant theory; stable curve Citations:Zbl 0534.14012 PDFBibTeX XMLCite \textit{E. Baldwin} and \textit{D. Swinarski}, IMRP, Int. Math. Res. Pap. 2008, Article ID rpn004, 104 p. (2008; Zbl 1155.14009) Full Text: DOI arXiv