Log canonical models for the moduli space of curves: The first divisorial contraction
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- by Brendan Hassett and Donghoon Hyeon PDF
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Abstract:
In this paper, we initiate our investigation of log canonical models for $(\overline {\mathcal {M}}_g,\alpha \delta )$ 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.References
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Additional Information
- Brendan Hassett
- Affiliation: Department of Mathematics, Rice University, 6100 Main St., Houston, Texas 77251-1892
- Email: hassett@math.rice.edu
- 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
- MR Author ID: 673409
- Email: hyeon@math.niu.edu, hyeond@marshall.edu
- Received by editor(s): November 28, 2007
- Published electronically: March 10, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 4471-4489
- MSC (2000): Primary 14E30, 14H10
- DOI: https://doi.org/10.1090/S0002-9947-09-04819-3
- MathSciNet review: 2500894