Regularity of powers of Stanley–Reisner ideals of one‐dimensional simplicial complexes

Nguyen Cong Minh and Thanh Vu

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3539-3558

Abstract: Let Δ be a one‐dimensional simplicial complex. Let IΔ$I_\Delta$ be the Stanley–Reisner ideal of Δ. We prove that for all s≥1$s \ge 1$ and all intermediate ideals J generated by IΔs$I_\Delta ^s$ and some minimal generators of IΔ(s)$I_\Delta ^{(s)}$, we have regJ=regIΔs=regIΔ(s).$$\begin{equation*} \hspace*{120pt}\operatorname{reg}J = \operatorname{reg}I_\Delta ^s = \operatorname{reg}I_\Delta ^{(s)}.\hspace*{-120pt} \end{equation*}$$

Date: 2023
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https://doi.org/10.1002/mana.202100485

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