Algebraic Geometry Seminar
Sonja Petrovic
UIC
Algebraic properties of cut ideals associated with ring graphs
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.
Friday August 29, 2008 at 4:00 PM in SEO 636