"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.

Seminar Archive

The WILDCATS Seminar is graciously supported by the University of Kentucky Department of Mathematics, the University of Kentucky Department of Statistics and the College of Arts and Sciences through the College Enrichment Fund.

The Discrete CATS seminar is supported in part by the University of Kentucky Department of Mathematics and the College of Arts and Sciences through the College Enrichment Fund. We also would like to thank Ben Braun and Richard Ehrenborg who continue to generously support our speakers with their NSF grants.

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