Log minimal model program for moduli spaces of pointed curves -- David Smyth, January 29, 2010

The space of Deligne-Mumford stable curves gives a beautiful compactification of the space of smooth curves which has connections to many areas of mathematics. In this talk, we will discuss alternate stability conditions for pointed elliptic curves in which the curve may acquire more exotic singularities such as cusps, tacnodes, and planar triple-points. Each of these alternate stability conditions gives rise to a birational contraction of the space of stable curves. In particular, we obtain sufficiently many contractions to run a certain log minimal model program on the space of stable curves.