University of Georgia
Mathematics Department Colloquium
Professor Michel Brion
Institut Fourier
January 9, 2003
Geometry of flag manifolds
Flag manifolds are projective algebraic varieties having many symmetries;
examples include projective spaces, quadrics, grassmanians....
The talk will discuss some basic questions on algebraic subvarieties of
complex flag manifolds. To any such variety, one can attach numerical
invariants that generalize the degree of a subvariety of projective space.
This raises the following problems, which are easy in projective space
and quite open in general: do there exist subvarieties with prescribed
numerical invariants? Among them, do there exist smooth ones? What about
subvarieties with the smallest numerical invariants?