Stability and equivariant maps

@article{Reichstein1989StabilityAE,
  title={Stability and equivariant maps},
  author={Zinovy Reichstein},
  journal={Inventiones mathematicae},
  year={1989},
  volume={96},
  pages={349-383}
}
  • Z. Reichstein
  • Published 1 June 1989
  • Mathematics
  • Inventiones mathematicae
SummaryConsider a linearized action of a reductive algebraic group on a projective algebraic varietyX over an algebraically closed field. In this situation Mumford [1] defined the concept of stability for points ofX. Given an equivariant morphismY→X we introduce a suitable linearization of the action onY and relate stability inY to stability inX. In particular, we prove a relative Hilbert-Mumford theorem which says that stability inX andY can be tested simultaneously by 1-parameter subgroups… 
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