A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps
نویسنده
چکیده
We construct the moduli spaces of stable maps, Mg,n(P , d), via geometric invariant theory. 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, Mg,n; this is valid over any base field. Our method follows that used in the case n = 0 by Gieseker in [6], to construct Mg, though our proof that the semistable set is nonempty is entirely different.
منابع مشابه
A GIT Construction of Moduli Spaces of Stable Maps in Positive Characteristic
In a previous paper, the author and David Swinarski constructed the moduli spaces of stable maps, Mg,n(P , d), via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction which this paper removes. We may now present the coarse moduli space of stable maps as a projective variety over a more general base field.
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تاریخ انتشار 2006