Log Canonical Models for the Moduli Space of Curves: First Divisorial Contraction Brendan Hassett and Donghoon Hyeon
نویسنده
چکیده
In this paper, we initiate our investigation of log canonical models for (Mg, αδ) as we decrease α from 1 to 0. We prove that for the first critical value α = 9/11, the log canonical model is isomorphic to the moduli space of pseudostable curves, which have nodes and cusps as singularities. We also show that α = 7/10 is the next critical value, i.e., the log canonical model stays the same in the interval (7/10, 9/11]. In the appendix, we develop a theory of log canonical models of stacks that explains how these can be expressed in terms of the coarse moduli space.
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