Towards a classification of modular compactifications of the moduli space of curves
Towards a classification of modular compactifications of the moduli space of curves

David Smyth, Harvard University
Fine Hall 322
The class of stable curves is deformationopen and satisfies the unique limit property, hence gives rise to the modular DeligneMumford compactification of $M_{g,n}$. But the class of stable curves is not unique in this respect; one obtains alternate compactifications by considering, for example, a moduli problem in which elliptic tails are replaced by cusps or in which marked points are allowed to collide. In this talk, we will survey progress toward a systematic classification of these alternate compactifications.