Seminar Algebra and Geometry: Elisa Gorla (Neuchâtel)

Universal Groebner bases and Cartwright-Sturmfels ideals

In this talk I will discuss a new idea for studying initial ideals and generic initial ideals of ideals in a polynomial ring graded over Z^m.

These ideas will then be applied to the study of universal Groebner bases of ideals of minors, which admit such a grading. The main tools and concepts are Z^m gradings, multigraded Hilbert series, universal Groebner bases, initial and generic initial ideals. I will introduce and study two families of multigraded ideals with the property that any two ideals in the same family that have the same Hilbert series also have the same generic initial ideal. I will show that ideals of minors belong to one of these families, and derive some result about their universal Groebner bases.

Veranstaltung übernehmen als iCal