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arXiv · 2109.06396

Regularity of powers of Stanley-Reisner ideals of one-dimensional simplicial complexes

Nguyen Cong Minh·Thanh Vu
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Abstract

Let $\Delta$ be a one-dimensional simplicial complex. Let $I_\Delta$ be the Stanley-Reisner ideal of $\Delta$. We prove that for all $s \ge 1$ and all intermediate ideals $J$ generated by $I_\Delta^s$ and some minimal generators of $I_\Delta^{(s)}$, we have $${\rm reg} J = {\rm reg} I_\Delta^s = {\rm reg} I_\Delta^{(s)}.$$

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Nguyen Cong Minh, Thanh Vu. 2021-09-14. Regularity of powers of Stanley-Reisner ideals of one-dimensional simplicial complexes. https://arxiv.org/abs/2109.06396

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