Induced nilpotent orbits and birational geometry

Details Induced nilpotent orbits and birational geometry Induced nilpotent orbits and birational geometry

2008-09-13

arxiv.org/abs/0809.2320v9

Advances in Mathematics, 222 (2009) 547-564

Mathematics

Algebraic Geometry

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 stateme

Scientific paper

10.1016/j.aim.2009.05.001

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.

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