Sonja Petrovic : Algebraic properties of cut ideals associated with ring graphs

Posted by Mihnea Popa , part of the Algebraic Geometry Seminar.

At

Aug. 29, 2008, 4 p.m.

In

SEO 636

Abstract

Given a graph G, any partition of its vertex set induces a coloring on its edges by recording whether the ends of an edge have been separated by the partition. The set of edges whose ends have been separated in this way is called a cut of the graph. These edge colorings induced by partitioning the vertex set parametrize a toric variety. Its defining ideal, the cut ideal of G, records algebraic relations among the cuts. These toric ideals were introduced by Sturmfels and Sullivant who also posed the problem of relating their properties to the combinatorial structure of the graph. We will describe a certain class of graphs whose cut ideals admit squarefree lexicographic Groebner bases. Thus, the associated semigroup algebras are Cohen-Macaulay, but not Gorenstein in general.