Faces of the edge cone of a bipartite graph

The affine toric varieties arising from bipartite graphs form an interesting subclass providing a rich connection between graph theory and algebraic geometry. An interesting question in the frame of toric varieties is the computation of their orbits under the corresponding torus action. In this subclass of toric varieties, one can use the connection to graph theory in order to answer this question. In this talk we provide a criterion for determining the torus orbits of these varieties by relating the faces of the corresponding edge cone to certain subgraphs of the bipartite graph.