Birational geometry and deformations of nilpotent orbits
Namikawa, Yoshinori
Duke Math. J., Tome 141 (2008) no. 1, p. 375-405 / Harvested from Project Euclid
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 ${E}_6$ , appear in the birational geometry for such orbits
Publié le : 2008-06-01
Classification:  14B07,  14M15,  14E30,  14J17,  17B45
@article{1211819166,
     author = {Namikawa, Yoshinori},
     title = {Birational geometry and deformations of nilpotent orbits},
     journal = {Duke Math. J.},
     volume = {141},
     number = {1},
     year = {2008},
     pages = { 375-405},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1211819166}
}
Namikawa, Yoshinori. Birational geometry and deformations of nilpotent orbits. Duke Math. J., Tome 141 (2008) no. 1, pp.  375-405. http://gdmltest.u-ga.fr/item/1211819166/