Dependence of Betti Numbers on Characteristic

Abstract

We study the dependence of graded Betti numbers of monomial ideals on the characteristic of the base field. The examples we describe include bipartite ideals and Stanley–Reisner ideals of vertex-decomposable complexes. We give a description of bipartite graphs and, using discrete Morse theory, provide a way of looking at the homology of arbitrary simplicial complexes through bipartite ideals.