Birational geometry and deformations of nilpotent orbits

Details Birational geometry and deformations of nilpotent orbits Birational geometry and deformations of nilpotent orbits

2006-11-06

arxiv.org/abs/math/0611129v10

Duke Math. Journal, Vol 143, (2008) 375-405

Mathematics

Algebraic Geometry

33 pages, revised

Scientific paper

10.1215/00127094-2008-022

This is a continuation of math.AG/0408274, where we have described the relative movable cone for a Springer resolution of the closure of a nilpotent orbit in a complex simple Lie algebra. But, in general, the movable cone does not coincide with the whole space of numerical classes of divisors on the Springer resolution. The purpose of this paper is, to describe the remainder. We shall first construct a deformation of the nilpotent orbit closure in a canonical manner according to Brieskorn and Slodowy, and next describe all its crepant simultaneous resolutions. This construction enables us to divide the whole space into a finite number of chambers. Moreover, by using this construction, one can generalize the main result of math.AG/0408274 to arbitrary Richardson orbits whose Springer maps have degree > 1. New Mukai flops, different from those of type A,D,E_6, will appear in the birational geometry for such orbits.

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