"Finiteness theorems for chains of toric ideals"

Abraham Martin del Campo
Texas A&M

Monday, November 16, 2009
4:00 pm, 845 Patterson Office Tower

Abstract:

We study chains of toric ideals that are invariant under a symmetric group action. In our setting, the ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus, these chains will fail to stabilize in the traditional commutative algebra sense. However, we prove a general theorem which says that "up to the action of the group", these chains stabilize up to monomial localization. This gives a partial resolution to a conjecture of Aschenbrenner and Hillar.

This is a joint work with Chris Hillar.