GIT CONSTRUCTIONS OF LOG CANONICAL MODELS OF Mg
نویسندگان
چکیده
The purpose of this article is to give an overview of the construction of compact moduli spaces of curves from the viewpoint of the log minimal model program forMg (now coined as the “Hassett-Keel” program). We will provide an update on new developments and discuss further problems. We have attempted to complement recent articles by Fedorchuk and Smyth [FS10] and Morrison [Mor09], and as a result our focus is put on the GIT construction of moduli spaces using low degree Hilbert points of curves. This method is expected to produce new compact moduli spaces of curves with increasingly worse singularities, and recent work by Ian Morrison and Dave Swinarski [MS11] is one solid step forward in this direction. The low-degree Hilbert quotients conjecturally realize various log canonical models of Mg
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