English

Classes of cut ideals and their Betti numbers

Commutative Algebra 2021-12-09 v1

Abstract

We study monomial cut ideals associated to a graph GG, which are a monomial analogue of toric cut ideals as introduced by Sturmfels and Sullivant. Primary decompositions, projective dimensions, and Castelnuovo-Mumford regularities are investigated if the graph can be decomposed as 00-clique sums and disjoint union of subgraphs. The total Betti numbers of a cycle are computed. Moreover, we classify all Freiman ideals among monomial cut ideals.

Keywords

Cite

@article{arxiv.2112.04239,
  title  = {Classes of cut ideals and their Betti numbers},
  author = {Jürgen Herzog and Masoomeh Rahimbeigi and Tim Römer},
  journal= {arXiv preprint arXiv:2112.04239},
  year   = {2021}
}