Tyrrell McAllister (Eindhoven):
Gelfand--Tsetlin polytopes and toric degenerations of
the invariants of n points in the projective plane
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 lattice
points in a cone over a certain Gelfand--Tsetlin polytope. We present
joint work with Howard showing that a similar strategy cannot work for
points in the projective plane P^2. In this 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.