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Combinatorics of the toric Hilbert scheme


Speaker: Diane Maclagan, UC Berkeley
Location: 693 Kerr
Start time: Wed, Dec 8 1999, 4:10PM

The toric Hilbert scheme parameterizes all ideals in a polynomial ring with the same multigraded Hilbert series as a given toric ideal. One central open problem on toric Hilbert schemes is whether they are always connected. I will describe joint work with Rekha Thomas (Texas A&M) which connects this question to the study of triangulations of a point configuration which are connected by bistellar flips (Pachner moves). We construct a graph on the monomial ideals in scheme which is connected if and only if the scheme is connected if and only if the scheme is connected.