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1 June 2008 Birational geometry and deformations of nilpotent orbits
Yoshinori Namikawa
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Duke Math. J. 143(2): 375-405 (1 June 2008). DOI: 10.1215/00127094-2008-022

Abstract

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

Citation

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Yoshinori Namikawa. "Birational geometry and deformations of nilpotent orbits." Duke Math. J. 143 (2) 375 - 405, 1 June 2008. https://doi.org/10.1215/00127094-2008-022

Information

Published: 1 June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1140.14004
MathSciNet: MR2420511
Digital Object Identifier: 10.1215/00127094-2008-022

Subjects:
Primary: 14B07 , 14E30 , 14M15
Secondary: 14J17 , 17B45

Rights: Copyright © 2008 Duke University Press

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Vol.143 • No. 2 • 1 June 2008
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