Noetherianity for infinite-dimensional toric ideals

Algebra Seminar
Monday, September 9, 2013 - 15:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Given a family of ideals which are symmetric under some group action on the variables, a natural question to ask is whether the generating set stabilizes up to symmetry as the number of variables tends to infinity. We answer this in the affirmative for a broad class of toric ideals, settling several open questions in work by Aschenbrenner-Hillar, Hillar-Sullivant, and Hillar-Martin del Campo. The proof is largely combinatorial, making use of matchings on bipartite graphs, and well-partial orders.