Geometric Invariant Theory for principal three-dimensional subgroups acting on flag varieties

@inproceedings{Seppanen2015GeometricIT,
  title={Geometric Invariant Theory for principal three-dimensional subgroups acting on flag varieties},
  author={Henrik Seppanen and Valdemar V. Tsanov},
  year={2015}
}
Let G be a semisimple complex Lie group. In this article, we study Geometric Invariant Theory on a flag variety G/B with respect to the action of a principal 3-dimensional simple subgroup S ⊂ G. We determine explicitly the GIT-equivalence classes of S-ample line bundles on G/B. We show that, under mild assumptions, among the GIT-classes there are chambers, in the sense of Dolgachev-Hu. The Hilbert quotients Y = X//S with respect to various chambers form a family of Mori dream spaces… 
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