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Graduate Student Seminar: "Why are homogeneous spaces projective varieties?" April 29, 2009
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Location: MSRI: Baker Board Room
Speaker(s) Charley Crissman
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If G is an affine algebraic group and H is a closed subgroup, when is G/H a variety? The answer -- rather surprisingly --
is always. Moreover, for a certain class of subgroups, called parabolic subgroups, the resulting quotient is actually a (smooth)
projective variety, called a "homogeneous space." Projective spaces, Grassmannians, and flag varieties are all examples of homogeneous spaces, but more exotic examples also exist. In this talk, I will explain how to see G/H as a variety, and will try to wave my hands in the general direction of some of the more interesting examples. If you already know what a parabolic subgroup is, expect to be thoroughly bored.

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