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Log canonical models for the moduli space of curves: The first divisorial contraction

Authors: Brendan Hassett and Donghoon Hyeon
Journal: Trans. Amer. Math. Soc. 361 (2009), 4471-4489
MSC (2000): Primary 14E30, 14H10
Published electronically: March 10, 2009
MathSciNet review: 2500894
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Abstract: In this paper, we initiate our investigation of log canonical models for $ (\overline{\bf\mathcal{M}}_g,\alpha \delta)$ as we decrease $ \alpha$ 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 $ (7/10, 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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Additional Information

Brendan Hassett
Affiliation: Department of Mathematics, Rice University, 6100 Main St., Houston, Texas 77251-1892

Donghoon Hyeon
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
Address at time of publication: Department of Mathematics, Marshall University, One John Marshall Drive, Huntington, West Virginia 25755

Received by editor(s): November 28, 2007
Published electronically: March 10, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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