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

<p>        

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.