English

Some homological properties of Borel type ideals

Commutative Algebra 2021-12-23 v1

Abstract

We study ideals of Borel type, including kk-Borel ideals and tt-spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated squarefree principal Borel ideals are computed. For the multiplicity, the result is given under an additional assumption which is always satisfied for squarefree principal Borel ideals. These results are used to analyze the behaviour of height, multiplicity and analytic spread of the homological shift ideals HSj(I)HS_j(I) as functions of jj, when II is an equigenerated squarefree Borel ideal.

Keywords

Cite

@article{arxiv.2112.11726,
  title  = {Some homological properties of Borel type ideals},
  author = {Jürgen Herzog and Somayeh Moradi and Masoomeh Rahimbeigi and Guangjun Zhu},
  journal= {arXiv preprint arXiv:2112.11726},
  year   = {2021}
}