| 概要 | The space of Deligne-Mumford stable curves gives a beautiful compactif
ication of the space of smooth curves which has connections to many areas of
mathematics. In this talk, we will discuss alternate stability conditions f
or pointed curves in which the curve may acquire more exotic singularities s
uch as cusps, tacnodes, and planar triple-points, and the marked points may
collide. Each of these alternate stability conditions gives rise to a birati
onal contraction of the space of Deligne-Mumford stable curves. In particula
r, we obtain sufficiently many contractions to run a minimal model program o
n the space of pointed stable curves of genus one. |