Induced nilpotent orbits and birational geometry
  In general, a nilpotent orbit closure in a complex simple Lie algebra \g, does not have a crepant resolution. But, it always has a Q-factorial terminalization by the minimal model program. According to B. Fu, a nilpotent orbit closure has a crepant resolution only when it is a Richardson orbit, and the resolution is obtained as a Springer map for it.   In this paper, we shall generalize this result to Q-factorial terminalizations when \g$ is classical. Here, the induced orbits play an important role instead of Richardson orbits. 
Yoshinori Namikawa