Induced nilpotent orbits and birational geometry
arXiv:0809.2320 · doi:10.1016/j.aim.2009.05.001
Abstract
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.
Lemma (1.2.4) is added. A little mistake in the proof of (1.4.3) is corrected. A Dynkin diagram has been missed in the statement of Prop (2.2.1); we add it in the new version. In the version 7, Lemma (1.1.1) and Example (2.3) are added. Version 8: The proof of (1.2.4) is corrected