Modular Contractions of M0,n
David Smyth, Harvard

Let M_{0,n} be the moduli space of n-pointed DM-stable curves of arithmetic genus zero. A modular contraction of M_{0,n} is, loosely speaking, a birational contraction M_{0,n} -> X, where X is itself the fine moduli space for a certain moduli problem (of curves). After making this definition precise, we'll classify all modular contractions of M_{0,n}. The moduli problems appearing in this classification will involve curves with worst-than-nodal singularities and colliding marked points. (The moduli spaces of weighted pointed curves introduced by Hassett will arise as a special case of this classification).