Induced nilpotent orbits and birational geometry

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

References in corpus (3)

• Symplectic singularities
• Symplectic Resolutions for Nilpotent Orbits
• Birational geometry and deformations of nilpotent orbits

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• On the affinization of a nilpotent orbit cover
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