David Smyth, Harvard University
New Modular Compactifications of M_{1,n}

We construct new compactifications of M_{1,n} by varying the definition of Deligne-Mumford stability to allow curves with cusps, tacnodes, triple-points, and more exotic singularities. In the spirit of Mori theory, we factor the rational maps between these new compactifications into elementary contractions and flips, and exhibit these spaces as log-canonical models of overline{M}_{1,n}.

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