Dependence of Betti Numbers on Characteristic

Details Dependence of Betti Numbers on Characteristic Dependence of Betti Numbers on Characteristic

2010-09-22

arxiv.org/abs/1009.4243v1

Mathematics

Commutative Algebra

8pp

Scientific paper

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, Stanley--Reisner ideals of vertex-decomposable complexes and ideals with componentwise linear resolutions. 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. We also prove that the Betti table of a monomial ideal over the field of rational numbers can be obtained from the Betti table over any field by a sequence of consecutive cancellations.

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