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Algebraic Geometry Seminar - Yoonsuk Hyun (KIAS)

posted Apr 15, 2012, 10:36 PM by Jihye Jung   [ updated Apr 15, 2012, 10:38 PM ]
- Title: Affine normal SL(2)-embeddings and flips
- Speaker : Yoonsuk Hyun(KIAS)
- Date & Time : April 13 (Fri) , 2012 14:00~ 15:00
- Place : Math Science building room 404
- Abstract
 : In this talk, I will talk about 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. Also, I 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.


One interesting properties of SL(2)-embeddings and GL(2)-embeddings are that they are Mori dream spaces with some general conditions. If time permitted, I will review how to describe the geometry of SL(2)-equivariant flips, and try to do the same thing for GL(2)-equivariant flips.