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

Donghoon Hyeon, Yongnam Lee

• 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 $M_3$.