A Compactification of the Space of Parametrized Rational Curves in   Grassmannians
  We construct an explicit compactification for the space of parametrized rational curves in a Grassmanian by a nonsingular projective variety such that the boundary is a divisor with simple normal crossings. This compactification is obtained by blowing up a Quot scheme successively along appropriate subschemes. 
Yijun Shao
math.AG