LOG CANONICAL MODELS FOR THE MODULI SPACE OF CURVES: THE FIRST DIVISORIAL CONTRACTION

Abstract

In this paper, we initiate our investigation of log canonical models for ((M) over barg, alpha delta) as we decrease ce from 1 to 0. We prove that for the first critical value alpha = 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 alpha = 7/10 is the next critical value, i.e., the log canonical model stays the same in the interval (7/1.0, 9/11]. In the appendix, we develop a theory of log canonical models of stacks that explains how these call be expressed in terms of the coarse moduli space.