English

Betti numbers of monomial ideals via facet covers

Commutative Algebra 2017-08-29 v2

Abstract

We give a sufficient condition for a monomial ideal to have a nonzero Betti number in each multidegree. In the case of facet ideals of simplicial forests, this condition becomes a necessary one and it allows us to characterize Betti numbers, projective dimension and regularity of such ideals combinatorially. Our condition is expressed in terms of minimal facet covers of simplicial complexes.

Keywords

Cite

@article{arxiv.1501.02496,
  title  = {Betti numbers of monomial ideals via facet covers},
  author = {Nursel Erey and Sara Faridi},
  journal= {arXiv preprint arXiv:1501.02496},
  year   = {2017}
}