English

Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone

Commutative Algebra 2011-02-19 v1

Abstract

When a cone is added to a simplicial complex Δ\Delta over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ\Delta'. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ\Delta' equals the projective dimension of the Stanley-Reisner ring of Δ\Delta' if the corresponding equality holds for Δ\Delta.

Keywords

Cite

@article{arxiv.0809.2194,
  title  = {Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone},
  author = {Margherita Barile and Naoki Terai},
  journal= {arXiv preprint arXiv:0809.2194},
  year   = {2011}
}