A compactification of the space of maps from curves
  We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper Deligne-Mumford stack equipped with a natural virtual fundamental class. 
Bumsig Kim, Andrew Kresch, Yong-Geun Oh
math.AG