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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.