2006/11/30 by Yoshinori Namikawa
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14Exx #msc:14Jxx #msc:17Bxx
paper · pdf · doi:10.1215/00127094-2008-022
published as Duke Math. Journal, Vol 143, (2008) 375-405 · 33 pages, revised
arxiv created 2007/08/27 · openalex publication_date 2008/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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