LOG MINIMAL MODEL PROGRAM FOR THE MODULI SPACE OF STABLE CURVES OF GENUS THREE

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 ((M) over bar (3), alpha delta) for each alpha is an element of [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 (M) over bar (g)(alpha), alpha is an element of [0, 1], with existing compactifications of M(3), some new and others classical, while the exception gives a new modular compactification of M(3).