GASC Seminar "Universal Groebner bases and Cartwright-Sturmfels ideals" by Elisa Gorla (University of Neuchâtel)

Abstract:  Universal Groebner bases are systems of generators of ideals, which are a Groebner basis with respect to any term order. In this talk, I will introduce a family of ideals named after Cartwright and Sturmfels and defined in terms of properties of their multigraded generic initial ideals. These ideals possess the remarkable property that all their initial ideals are radical. Moreover, the family of Cartwright-Sturmfels ideals is closed under several natural operations, including elimination and taking linear sections. Their natural "dual" family also possesses remarkable properties, including the fact that every (multigraded) minimal system of generators is a universal Groebner basis. A connection to universal Groebner bases for determinantal ideals will be discussed.