# Mathematics Colloquia and Seminars

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### Combinatorics of the toric Hilbert scheme

**Geometry/Topology**

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.