English

Powers of generalized binomial edge ideals of path graphs

Commutative Algebra 2023-11-01 v1

Abstract

In this article, we study the powers of the generalized binomial edge ideal JKm,Pn\mathcal{J}_{K_m,P_n} of a path graph PnP_n. We explicitly compute their regularities and determine the limit of their depths. We also show that these ordinary powers coincide with their symbolic powers. Additionally, we study the Rees algebra and the special fiber ring of JKm,Pn\mathcal{J}_{K_m,P_n} via Sagbi basis theory. In particular, we obtain exact formulas for the regularity of these blowup algebras.

Keywords

Cite

@article{arxiv.2310.20235,
  title  = {Powers of generalized binomial edge ideals of path graphs},
  author = {Yi-Huang Shen and Guangjun Zhu},
  journal= {arXiv preprint arXiv:2310.20235},
  year   = {2023}
}