Mathematics – Algebraic Geometry
Scientific paper
2004-04-05
Mathematics
Algebraic Geometry
30 pages, Several errors are corrected
Scientific paper
In this paper, we shall prove that any two (projective) symplectic resolutions of a nilpotent orbit closure in a classical simple Lie algebra are connected by a finite sequence of diagrams which are locally trivial families of Mukai flops of type A or of type D. A Mukai flop of type A is the same as a stratified Mukai flop in our previous paper "Mukai flops and derived categories II". On the other hand, a Mukai flop of type D comes from a nilpotent orbit in so(2k). Let G^+ and G^- be two connected components of the orthogonal Grassmannian G_{iso}(k,2k). Then the closure of this orbit has two Springer resolutions via the cotanegent bundles T^*G^+ and T^*G^-, which is the Mukai flop of type D. Our result would clarify the geometric meaning of the results of Spaltenstein and Hesselink. To illustrate this, three examples will be given. Another purpose of this paper is to give an affimative answer to a conjecture in the paper "Uniqueness of crepant resolutions and symplectic singularities" math.AG/0306091, for nilpotent orbit cases. A key idea is the notion of a "Dixmier sheet" studied by Borho and Kraft.
No associations
LandOfFree
Birational Geometry of symplectic resolutions of nilpotent orbits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Birational Geometry of symplectic resolutions of nilpotent orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Birational Geometry of symplectic resolutions of nilpotent orbits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-666694