On affine embeddings of reductive groups

Abstract

In this thesis, we study the properties and the classification of embeddings of homogeneous spaces, especially the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, some specific subset of one-parameter subgroups may contribute to the classification of affine embeddings of general reductive group. To check this, we review the theory of affine normal SL(2)-embeddings, and prove that the classification cannot be solved entirely based on one-parameter subgroups. We can also show that even though this set does not give a complete answer to the classification problem, but still contains useful information about varieties. We will also give examples of GL(2)- embeddings which had not previously been constructed in detail, which might be helpful in understanding the general classification of affine normal G-embeddings.