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.
Supported by the Erwin Schrödinger Institute, Vienna, Austria
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Snow, D. (2004). The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties. In: Popov, V.L. (eds) Algebraic Transformation Groups and Algebraic Varieties. Encyclopaedia of Mathematical Sciences, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05652-3_9
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DOI: https://doi.org/10.1007/978-3-662-05652-3_9
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