Abstract for the talk on 19.11.2019 (11:00 h)Seminar on Nonlinear Algebra
Antonio Macchia (Freie Universität Berlin)
Binomial edge ideals of bipartite graphs
19.11.2019, 11:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, G3 10 (Hörsaal)
Binomial edge ideals are ideals generated by binomials corresponding to the edges of a graph, naturally generalizing the ideals of 2-minors of a generic matrix with two rows. They also arise in Algebraic Statistics in the context of conditional independence ideals. We give a combinatorial classification of Cohen-Macaulay binomial edge ideals of bipartite graphs providing an explicit construction in graph-theoretical terms. In the proof we use the dual graph of an ideal, showing in our setting the converse of Hartshorne’s Connectedness theorem. As a consequence, we prove for these ideals a Hirsch-type conjecture of Benedetti-Varbaro.
This is a joint work with Davide Bolognini and Francesco Strazzanti.