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Gelfand--Tsetlin polytopes and toric degenerations of the invariants of n points in the projective plane.Algebra & Discrete Mathematics
|Speaker: ||Tyrrell B. McAllister, Eindhoven University of Technology|
|Location: ||1147 MSB|
|Start time: ||Thu, Apr 5 2007, 12:10PM|
Howard, Millson, Snowden, and Vakil bounded the degrees of relations generating the
ring of invariants of n points on the projective line P^1 by studying the toric degeneration to
the semi-group algebra of the cone over an associated Gelfand--Tsetlin polytope. We present
work in progress with Howard showing that a similar strategy is much less effective for points
in the projective plane. In this latter case, we can show that the ring of invariants is
generated in degree O(n^5). However, the toric degeneration to the corresponding
Gelfand--Tsetlin semi-group algebra introduces generators of exponential degree. We show this
by exhibiting vertices of the GT polytope with exponential denominators.
Note special day and time. Regular seminar time this quarter is Fridays at 3pm.