The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties

  • Dennis Snow
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 132)


Let G be a connected linear algebraic group over ℂ and let H a closed algebraic subgroup. A fundamental problem in the study of homogeneous spaces is to describe, characterize, or classify those quotients G/H that are affine varieties. While cohomological characterizations of affine G/H are possible, there is still no general group-theoretic conditions that imply G/H is affine. In this article, we survey some of the known results about this problem and suggest a way of classifying affine G/H by means of its internal geometric structure as a fiber bundle.


Homogeneous Space Algebraic Group Unipotent Radical Reductive Subgroup Homogeneous Vector Bundle 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Dennis Snow
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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