Duke Mathematical Journal

Birational geometry and deformations of nilpotent orbits

Yoshinori Namikawa

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This is a continuation of [N2], 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 article is to describe the remainder. We first construct a deformation of the nilpotent orbit closure in a canonical manner, according to Brieskorn and Slodowy (see [S]), 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 [N2] to arbitrary Richardson orbits whose Springer maps have degree greater than 1. New Mukai flops, different from those of types A, D, and E6, appear in the birational geometry for such orbits

Article information

Duke Math. J. Volume 143, Number 2 (2008), 375-405.

First available in Project Euclid: 26 May 2008

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Zentralblatt MATH identifier

Primary: 14B07: Deformations of singularities [See also 14D15, 32S30] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14J17: Singularities [See also 14B05, 14E15] 17B45: Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]


Namikawa, Yoshinori. Birational geometry and deformations of nilpotent orbits. Duke Math. J. 143 (2008), no. 2, 375--405. doi:10.1215/00127094-2008-022. https://projecteuclid.org/euclid.dmj/1211819166

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