Toric geometry of series-parallel graphs

Combinatorics Seminar
Friday, April 17, 2009 - 15:00
1 hour (actually 50 minutes)
Skiles 255
Georgia State University
Let G be a graph and K be a field. We associate to G a projective toric variety X_G over K, the cut variety of the graph G. The cut ideal I_G of the graph G is the ideal defining the cut variety. In this talk, we show that, if G is a subgraph of a subdivision of a book or an outerplanar graph, then the minimal generators are quadrics. Furthermore we describe the generators of the cut ideal of a subdivision of a book.