Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14E30, 14H10

Retrieve articles in all journals with MSC (2000): 14E30, 14H10


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
Email: hyeon@math.niu.edu, hyeond@marshall.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04819-3
PII: S 0002-9947(09)04819-3
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.