Geometric invariant theory for principal three-dimensional subgroups acting on flag varieties

  • Henrik Seppänen

    Georg-August Universität Göttingen, Germany
  • Valdemar V. Tsanov

    Georg-August Universität Göttingen, Germany
Geometric invariant theory for principal three-dimensional subgroups acting on flag varieties cover
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Abstract

Let GG be a semisimple complex Lie group. In this article, we study Geometric Invariant Theory on a flag variety G/BG/B with respect to the action of a principal 3-dimensional simple subgroup SGS\subset G. We determine explicitly the GIT-equivalence classes of SS-ample line bundles on G/BG/B. We show that, under mild assumptions, among the GIT-classes there are chambers, in the sense of Dolgachev-Hu. The GIT-quotients with respect to various chambers form a family of Mori dream spaces, canonically associated with GG. We are able to determine the three important cones in the Picard group of any of these quotients: the pseudoeffective-, the movable-, and the nef cones.