• DOI:10.1007/S00031-008-9022-0
• Corpus ID: 17832865

Descent of Line Bundles to Git Quotients of Flag Varieties by Maximal Torus

@article{Kumar2007DescentOL,
  title={Descent of Line Bundles to Git Quotients of Flag Varieties by Maximal Torus},
  author={Shrawan Kumar},
  journal={Transformation Groups},
  year={2007},
  volume={13},
  pages={757-771},
  url={https://api.semanticscholar.org/CorpusID:17832865}
}

• Shrawan Kumar
• Published 19 February 2007
• Mathematics
• Transformation Groups

Let G be a connected, simply connected semisimple complex algebraic group with a maximal torus T and let P be a parabolic subgroup containing T. Let $ \mathcal{L}_{P} {\left( \lambda \right)} $ be a homogeneous ample line bundle on the ag variety Y = G = P. We give a necessary and sufficient condition for $ \mathcal{L}_{P} {\left( \lambda \right)} $ to descend to a line bundle on the GIT quotient Y(λ)//T. As a consequence of this result, we get the precise list of P-regular weights λ for which… 

Let G be a connected, simply connected semisimple complex algebraic group with a maximal torus T and let P be a parabolic subgroup containing T. Let $ \mathcal{L}_{P} {\left( \lambda \right)} $ be a homogeneous ample line bundle on the ag variety Y = G = P. We give a necessary and sufficient condition for $ \mathcal{L}_{P} {\left( \lambda \right)} $ to descend to a line bundle on the GIT quotient Y(λ)//T. As a consequence of this result, we get the precise list of P-regular weights λ for which the line bundle $ \mathcal{L}_{P} {\left( \lambda \right)} $ descends to the GIT quotient Y(λ)//T.