The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties
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.
KeywordsHomogeneous Space Algebraic Group Unipotent Radical Reductive Subgroup Homogeneous Vector Bundle
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