Binomial edge ideals

Monday, September 11, 2017
Dott.Francesco Strazzanti
University of Sevilla


In the last decades the connections between commutative algebra and combinatorics have been extensively explored. It is interesting to study classes of ideals in a polynomial ring associating with them combinatorial objects, such as simplicial complexes, graphs, clutters or polytopes.

In this talk we are interested in the so-called binomial edge ideals, which are ideals generated by binomials corresponding to the edges of a finite simple graph G. They can be viewed as a generalization of the ideal of 2-minors of a generic matrix with two rows.

In particular, we provide a classification of Cohen-Macaulay binomial edge ideals of bipartite graphs, giving an explicit construction in graph-theoretical terms.

To prove this classification we make use of the dual graph of an ideal, showing in our setting the converse of Hartshorne's Connectedness Theorem.