Alternate Compactifications of Moduli Spaces of Curves

Abstract

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber decompositions of $\M_{g,n}$.

86 pages. Revised version. Submitted to Handbook of Moduli, Farkas and Morrison, eds

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• An outline of the log minimal model program for the moduli space of curves