Mathematical Research Letters

Volume 17 (2010)

Number 4

Log minimal model program for the moduli space of stable curves of genus three

Pages: 625 – 636

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n4.a4

Authors

Donghoon Hyeon (Postech, Pohang, Gyungbuk, 790-784, Republic of Korea)

Yongnam Lee (Sogang University, Sinsu-dong, Mapo-gu, Seoul 121-742, Republic of Korea)

Abstract

We completely carry out the log minimal model program for the moduli space of stable curves of genus three with respect to the total boundary $\delta$: We give a modular interpretation of the log canonical model for the pair $(\bar{\mathcal M}_3, \a\d)$ for each $\a \in [0,7/10)$ and of the birational maps between them. By using the modular description, we are able to identify all but one log canonical models $\Mg(\a)$, $\a \in [0,1]$, with existing compactifications of $M_3$, some new and others classical, while the exception gives a new modular compactification of $M_3$.

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