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Tuesday, June 27, 2006

**Abstract:** In algebraic geometry, we often need to study all geometric objects of a certain type, e.g. all hyperplanes in a fixed projective space, or all lines in a fixed projective space, or all elliptic curves up to isomorphism. At this level of detail, we are only considering the set of all such objects. But there is a natural way to endow this set with an algebraic structure (or analytic structure if you're a complex geometer), arriving at, in the above examples, dual projective spaces, Grassmannians, and the moduli space of elliptic curves. This is an elemantary talk, and will assume only basic familiarity with algebraic or complex geometry.