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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)

Abstract

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.

Keywords

Homogeneous Space Algebraic Group Unipotent Radical Reductive Subgroup Homogeneous Vector Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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