A geometric invariant theory construction of moduli spaces of stable maps

Details A geometric invariant theory construction of moduli spaces of stable maps A geometric invariant theory construction of moduli spaces of stable maps

2007-06-11

arxiv.org/abs/0706.1381v3

International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn004, 104 pages

Mathematics

Algebraic Geometry

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

Scientific paper

10.1093/imrp/rpn004

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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